Please answer it :(a) Simplify trigonometric expressions using trigonometric identities; andb) Prove other trigonometric identities using fundamental trigonometric identities.
1. Please answer it :(a) Simplify trigonometric expressions using trigonometric identities; andb) Prove other trigonometric identities using fundamental trigonometric identities.
multiply (cos x/ 1+ sin x ) to (1-sin x/ 1- sin x)
cos x (1-sin x)/ 1-sin²x
cos x (1-sin x)/ cos² x
cos x (1-sin x)/ cos x(cos x)
cancel the cos x in the numerator and one of the cos x in the denominator
(1-sin x)/cos x will be the answer
2. how to prove trigonometric identities
by pythagorean theorem when raduis or hypo is 1 or 1unit circle formula when (0,0) at the center of the circle; when x is a function of cos and y is sine; -ratio -gen formula( sum ,product, dif., double and half angle formula and find other relation in proving identities
3. prove the given trigonometric identity (full solution)
Answer:
Proving the problems on trigonometric identities:
• ( 1 - sin A)/(1 + sin A) = (sec A - tan A)2 Solution: L.H.S = (1 - sin A)/(1 + sin A) ...
•Prove that, √{(sec θ – 1)/(sec θ + 1)} = cosec θ - cot θ. Solution: L.H.S.= √{(sec θ – 1)/(sec θ + 1)} ...
•tan4 θ + tan2 θ = sec4 θ - sec2 θ
4. Prove using trigonometric identities cos/ 1+ sin = 1-sin/ cos
Answer:
tan θ = sin θ
cos θ and cot θ = cos θ
sin θ .
Step-by-step explanation:hope it helped u out..
5. How to solve trigonometric identities easily?
Answer:
follow and understands the required
6. prove the trigonometric identity [tex]\csc (x)=\sin(x)\cot^2(x)+\sin(x)[/tex] please wag pong trial and error
Answer:
[tex]\sf R.H.S = sin(x)cot^2(x)+sin(x)[/tex]
[tex]\implies \sf R.H.S = sin(x)(cot^2(x)+1)[/tex]
[tex]\implies \sf R.H.S = sin(x)(csc^2(y))[/tex]
[tex]\implies \sf R.H.S = sin(x)((\frac{1}{sin(x)})^2)[/tex]
[tex]\implies \sf R.H.S = sin(x)(\frac{1}{sin^2(x)})[/tex]
[tex]\implies \sf R.H.S = \frac{sin(x)}{sin^2(x)}[/tex]
[tex]\implies \sf R.H.S = \frac{1}{sin(x)}[/tex]
[tex]\implies \sf R.H.S = csc(x)[/tex]
[tex]\therefore \sf R.H.S = L.H.S[/tex]
#CarryOnLearning
7. prove the trigonometric identities. (1+sec x)(1-cos x)=tan x sin x
(1 + 1/cosx)(1-cosx) = tanxsinx
1 - cosx + 1/cosx -1 = (sinx/cosx)(sinx)
(-cos^(2) x + 1)/cosx = (sin^(2) x)/cosx
[tex] \frac{ sin^{2} x }{cosx} = \frac{ sin^{2} x }{cosx} [/tex]
8. proving Trigonometric Identities secx - cosx= tanxsinx please answer
secx - cos x = tanxsinx
1/cosx - cos x = tanxsinx
1 - cos^2x = tanxsinx
cosx
sin^2x = tanxsinx
cosx
sinxsinx = tanxsinx
cosx
tanxsin = tanxsinx
9. 3. What is the difference between verifying a trigonometric identity andsolving a trigonometric equation?
Answer:
Trigonometric identities describe equalities between related trigonometric expres- sions while trigonometric equations ask us to determine the specific values of the variables that make two expressions equal.
10. Give 2 examples of proving trigonometric identities. Provide solutions and brief explanations.
2 example of proviing is the name that i known
11. INSTRUCTION: Prove the trigonometric identities.PS. Help me and I'll mark you the brainliest
Answer:
hanap ka babae
Step-by-step explanation:
kiss mo hanap Mona din ako Ng babae
12. Proving trigonometric identities csc x - sin x / cos x = cot x
(csc x - sin x)/ cox = cotx (original equation)
sinx csc x- sin x² =cos x² (cross multiply)
sinx cscx=1 (identity value)
cosx ²+sinx ²=1 (identity value, transposed)
13. Prove [tex] \frac{ \sin(4a) + \sin(6a) }{ \cos(4a) - \cos(6a) } = \cot(a) [/tex]Formula from Trigonometric Identities
Step-by-step explanation:
i need it too please help
14. when to use trigonometric identities?
You only use trigonometric identities when you face parts like bearing and polar graphing. Especially on triangles, find the angle find the length of parts, etc. Trigonometry mostly focuses on triangles... Hope this helps =)
15. PROVE THE FOLLOWING TRIGONOMETRIC IDENTITES WITH SOLUTION
✒️TRIGONOMETRY
[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]
[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]
Know that the tangent of an angle is as same as the ratio of the sine of the same angle to the cosine of the same angle.
[tex] \begin{align} & \bold{Identity:} \\ & \quad \boxed{\rm \tan\theta = \frac{\sin\theta}{\cos\theta}} \end{align} [/tex]
Plug it in to the given equation.
[tex] \frac{\tan x - \sin (\text-x)}{1 + \cos x} = \tan x \\ [/tex][tex] \frac{\frac{\sin x}{\cos x} - \sin (\text-x)}{1 + \cos x} = \tan x \\ [/tex]Another identity says that the sine of a negative angle is also the negative sign of the positive value of the angle.
[tex] \begin{align} & \bold{Identity:} \\ & \quad \boxed{\rm \sin (\text-\theta) = \text-\sin \theta} \end{align} [/tex]
Plug it in to the equation.
[tex] \frac{\frac{\sin x}{\cos x} - (\text- \sin x)}{1 + \cos x} = \tan x \\ [/tex][tex] \frac{\frac{\sin x}{\cos x} + \sin x}{1 + \cos x} = \tan x \\ [/tex]Write it in horizontal division so I can solve it easily in here. (Optional)
[tex] \small \bigg(\frac{\sin x}{\cos x} + \sin x\bigg) \div (1 + \cos x) = \tan x \\ [/tex][tex] \small \bigg(\frac{\sin x}{\cos x} + \frac{\sin x (\cos x)}{\cos x}\bigg) \div (1 + \cos x) = \tan x \\ [/tex][tex] \small \frac{\sin x + \sin x(\cos x)}{\cos x} \div (1 + \cos x) = \tan x \\ [/tex]Dividing fractions is as same as multiplying the fraction to the reciprocal of the divisor.
[tex] \frac{\sin x + \sin x(\cos x)}{\cos x} \times \frac1{1 + \cos x} = \tan x \\ [/tex][tex] \frac{\sin x + \sin x(\cos x)}{\cos x( 1 + \cos x)} = \tan x \\ [/tex]Factor out the sine of x then cancel the sum of 1 and the cosine of x.
[tex] \frac{\sin x( 1+ \cos x)}{\cos x( 1 + \cos x)} = \tan x \\ [/tex][tex] \frac{\sin x}{\cos x} = \tan x \\ [/tex]As we have proved, the ratio of the sine of x to the cosine of x is equal to the tangent of x.
[tex] \tan x = \tan x \:\quad \rm (TRUE)[/tex][tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]
(ノ^_^)ノ
16. trigonometric identities examples
(sin x + cos x) (tan x + cot x) = sec x + csc x
tan x + cot x = sec x csc x
1 + cot² x = csc² x
1 + cot² x = csc² x
17. Prove the equality using Trigonometric Identities. COMPLETE SOLUTION
Step-by-step explanation:
[tex] \frac{sin \: x \: cos \: x \: + sin \: x}{cos x\: + cos {}^{2} x} = tan \: x \\ \\ \frac{sin \: x(cos \: x + 1)}{cos \: x(1 + cos \: x)} = tan \: x \\ \\ \frac{sin \: x}{cos \: x \: } = tan \: x \\ \\ tan \: x = tan \: x[/tex]
18. Trigonometric identities: Reciprocal Quotient Pythagorean identities
u mean how u got this 3 ?
or we can derive this using one unit circle formula ,
1) reciprocal, the ineverse trig function of a rigth triangle; cos=1/sec....
2.)quotient , where tangent is equal y/x ( x=cos, x=sin)polar coordinates by 1 unit circle formula; tan=sin/cos
3.) pythagorean identities, u can use the above two function as x=cos , y=sin , where c=raduis 1 at 1 unit circle formula; r^2=x^2 +y^2; 1=x^2 +y^2;
since x=cos, y=sin ,thus we have : sin^2 +cos^2 =1
19. Prove the trigonometric identities :1 - tan²x ________ = 1 - 2 sin²x1 + tan²x
Answer:
[tex] \frac{1 - {tan}^{2}x }{1 + {tan}^{2}x } = 1 - 2 {sin}^{2} x[/tex]
since:
[tex]1 + {tan}^{2} x = {sec}^{2} x[/tex]
[tex] \frac{1 - {tan}^{2} x}{ {sec}^{2}x } = 1 - 2 {sin}^{2} x[/tex]
[tex] \frac{1}{ {sec}^{2} x} - \frac{ {tan}^{2}x }{ {sec}^{2} x} = 1 - 2{sin}^{2} x[/tex]
[tex] {sec}^{2} x = \frac{1}{ {cos}^{2}x } [/tex]
[tex] {tan}^{2} x = \frac{ {sin}^{2}x }{ {cos}^{2}x } [/tex]
[tex] \frac{1}{ \frac{1}{ {cos}^{2} x} } - \frac{ \frac{ {sin}^{2} x}{ {cos}^{2} x} }{ \frac{1}{ {cos}^{2}x } } = 1 - 2 {sin}^{2} x[/tex]
arrange:
[tex] \frac{1}{1} \times \frac{ {cos}^{2} x}{1} = {cos}^{2} x[/tex]
[tex] \frac{ {sin}^{2}x }{ {cos}^{2} x} \times \frac{ {cos}^{2} x}{1} = {sin}^{2} x[/tex]
insert:
[tex] {cos}^{2} x - {sin}^{2} x = 1 - 2 {sin}^{2} x[/tex]
since:
[tex] {cos}^{2} x = 1 - {sin}^{2} x[/tex]
therefore:
[tex](1 - {sin}^{2} x) - {sin}^{2} x = 1 - 2 {sin}^{2} x[/tex]
[tex]1 - 2 {sin}^{2} x = 1 - 2 {sin}^{2} x[/tex]
20. Prove the trigonometric identity: [tex]\frac{tanx^{2}x -1}{tanx^{2}x +1} =1-2 cos^{2}x[/tex]
Answer:
haha di ako mahilig sa math na diko pa napagaralan grade 6 p.o. palang ako
21. prove the given trigonometric identity(full solution)
SOLUTION:
For [tex] \cos \theta - \frac{\cos \theta}{1- \tan \theta} = \frac{\sin A \cos \theta }{\sin A - \cos \theta} [/tex] we substitue 0 for [tex] \theta [/tex]
For [tex] \cos \theta - \frac{\cos \theta}{1- \tan \theta} = \frac{\sin A \cos \theta }{\sin A - \cos \theta} [/tex] we substitute 1 for [tex] A [/tex]
[tex] \rm{ cos \ 0 - \frac{cos \ 0}{1 - tan \ 0} = \frac{sin \ 1 \ cos \ 0}{sin \ 1 \ - \ cos \ 0}} \\\\ \rm{0 = \frac{sin(1)}{sin(1)-1}} \\\\ \rm{\therefore \ False} [/tex]Hope this helps
22. Paano po mag-prove ng trigonometric identities?
Answer:
Proving Trigonometric Identities - Basic
In order to prove trigonometric identities, we generally use other known identities such as Pythagorean identities. Prove that ( 1 − sin x ) ( 1 + csc x ) = cos x cot x .
Answer:
In order to prove trigonometric identities, we generally use other known identities such as Pythagorean identities. Prove that ( 1 − sin x ) ( 1 + csc x ) = cos x cot x
Step-by-step explanation:
1) Always Start from the More Complex Side
2) Express everything into Sine and Cosine
3) Combine Terms into a Single Fraction
4) Use Pythagorean Identities to transform between sin²x and cos²x
5) Know when to Apply Double Angle Formula (DAF)
6) Know when to Apply Addition Formula (AF)
7) Good Old Expand/ Factorize/ Simplify/ Cancelling
8) Take one Step, Watch one step.
9) When Desperate… Pretend!
Disclaimer: Only use this tactic if you find yourself stuck half way during the trigo proving process in an examination (with the clock ticking away) and you do not want to jeopardize the rest of the paper.
10) Practice! Practice! Practice!
11) Do not try to Prove a Question that says “Solve”!
23. What are the fundamentaltrigonometric identities?
Answer:
The sine, cosine, and tangent.Step-by-step explanation:
Sine Function: sin(θ) = Opposite / Hypotenuse
Cosine Function: cos(θ) = Adjacent / Hypotenuse
Tangent Function: tan(θ) = Opposite / Adjacent
24. proving each trigonometric identities tan× sin× = sec×-cos×
math
Step-by-step explanation:
cos+con-=lest
sana po maka tulong
25. prove trigonometric identity of sin x sec x = tan x
Pabrainliest po ayan napo sagot nasa pic na po kokopyahinnnalang
26. prove that sin theta is identity to (cot theta) x ( tan theta ) *trigonometric identities
cot A x tan A = cos A/sin A x sin A/cos A = 1
this is not an identity as sin A and 1 is not identical
but it could be an equation
if sin A = 1
then A = 90 degree
27. prove the trigonometric identity above. show your solution.
Answer:
The provided question is not an IDENTITY
Step-by-step explanation:
[tex] \frac{csc(0)}{cos(0) - 1} + \frac{csc(0)}{ar0 + 1} = 2 \: sec ^{2} \: 0[/tex]
Answer: the equation of the question is true
nasa pic po ang solution. salamat po
the equation of the question is true
#CarryOnLearning
28. Prove the following trigonometric identity cot x tanx
Answer:
where's the given problem?
Step-by-step explanation:
carry on learning, hope it helps
29. Prove the Trigonometric Identity given:1 / 1+cosx + 1 / 1−cosx = 2csc²xps. really need help with this one, plss. thank uu
Answer:
0.89()+7) -7(44r)+5;7⁷
30. How can we prove this Trigonometric identity??? secФ = [tex] \\ \frac{sinФ}{cotФ \frac} [/tex] + cosФ
secФ=[tex] \frac{sin ^{2} }{cos} [/tex]+cos
secФ=[tex] \frac{sin ^{2}+cos ^{2} }{cos} [/tex]
secФ=[tex] \frac{1}{cos} [/tex]
secФ=secФ
I hope na gets mo yan,pythagorian at reciprocal identity yan
