Use Euler's identity to (a) show the identities (i) cos(@ + B) =cos(a) cos(B) –- sin(a) sin(B), (ii) sin(a +B)= sin(a) cos(B) + cos(a) sin(B);

Q: Verify the identity. sin +0 = cos 0 0 2

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Q: Express (cos(a@) ti sin 4i sin (a@) in exponential form

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Q: Show that the following is true. cos(X-pi/2) = sinX

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Q: In order for sin-1 (sin x)= x, x must be a value between ____ and ____.

A: In order for sin-1sinx=x, x must be a value between ___ and ___.

Q: Prove the identity. +x + sin 6. sin = cos x

A: Given, We have to prove the identity sinπ6+x+sinπ6-x=cosx

Q: Find the exact value of cos2 15° - sin2 15°.

A: We have to find the exact value of cos2 15°-sin2 15°Formula used :-Cos 2θ= cos2 θ-sin2θ -1

Q: Find sin 2x, cos 2x, and tan 2x if sin x - and x terminates in quadrant II- sin 2x %3D cos 2x %3D…

A: Use the fact that in second quadrant cos and tan are negative.

Q: 1- Determine. 4. Cos 'x sinX dx

A: Given:                     ∫cos4(x) sin(x) dx     Solution:                    Integrating the given…

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = - cos(x) > 0 sin(2x) =…

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Q: If sin A = with A in QII, find Cos 9 cos Cos COS Cos Cos 스2

A: cos2A +sin2A =1 cos(2A)=2 cos2A -1

Q: Find sin 2x, cos 2x, and tan2x if tanx = and x terminates in guadrant II. sin 2x ? cos 2.x tan 2x…

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Q: Find sin(2x), cos(2x), and tan(2x) from the given informa 15 tan(x) x in Quadrant II 8 240 sin(2x) =…

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Q: PROVE that sin x = V1 – cos² x is NOT an identity. -

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Q: Prove the identity sin(-0)- cos (+0)

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Q: Verify the identity. sin 0-1 tan 0- sec 0 %3D cos e

A: Here we use basic identities of trigonometric ratios.

Q: Verify sin (x +) = cos(n – x) %3D

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Q: Verify the identity.

A: We have  cosx-5π2=sinx   It is known that cosA-B=cosAcosB+sinAsinB   Consider LHS:…

Q: snip

A: Our Aim is to establish the identity given below:-1-sinθcos (θ)=cos (θ)1+sinθ-(i)

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = - cos(x) > 0 sin(2x) cos(2x)…

A: Given,           tan(x) =-16, cos(x) > 0

Q: Find sin 5, given that sin x = 2 i and 0<x<5.

A: Here  sin x=14⇒cos x=1-sin2x              ⇒cos x=1-116              ⇒cos x=154 Now, sin2x2=1- cos x2…

Q: Use De Moivre's Theorem with n= 3 to express cos 3θ and sin 3θ in terms of cos θ and sin θ.

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Q: (a) Prove that Sin-1x  + Cos-1 x  = π/2 .(b) Use part (a) to prove Formula 6.

A: a) We have to prove sin-1x+cos-1x=π2 Let sin-1x=θ                                     ⋯⋯1…

Q: 5. cos A =- and sin B =, both A and B in QIl. 6. cos A = - and cos B = - 2, with A and B in QIII. 17

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Q: Find sin - and cos 2' given that cos 0 and 0<0 < 3

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find the value of x between 0° and 180° such that 2 sin(x+ 30°) = cos(x-45°). %3D

A: You know:

Q: Verify the identity. 2 sin(x) cos(x) = 1 (sin(x) + cos(x))2 - 1

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Q: Given that sin2   x + cos2  x = 1 and sin x = −√2/5, what is the possible value of cos x

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Q: Given that sin-(x) = a and cos-(x) = B show that sin(a + B) = 1. %3D

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Q: Find a value of x that satisfies the equation cos 12° = sin (x). %3D

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Q: Prove that: Sin'x+ cosx=I

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Q: Which is equal to (sin⁡x+cos⁡x)^2+(sin⁡x−cos⁡x)^2 using identities?

A: Now we use identity  Sin2x +cos2x =1 And formula (a+b)2= a2 +b2 + 2ab  (a-b)2 = a2 + b2 - 2ab

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. 3T 2 sin(2x) sin(x) = = cos(2x) =…

A: We have to solve above question and find sin cos and tan value

Q: Use De Moivre’s Theorem with n = 3 to express cos 3θ and sin 3θ in terms of cos θ and sinθ.

A: To express cos3θ and sin 3θ in terms of cosθ and sinθ, using De Moivre's theorem with n=3. De…

Q: PROVE that sin x = v1 – cos² x is NOT an identity.

A: Topic:- trigonometry

Q: Verify that the equation is an identity. 1 1 1- sin x 1+ sin x COS

A: We need to verify the identity:11-sinx+11+sinx=2cos2x

Q: . is cos(cos^-1 1.7=1.7 true?     2. is sin^-1 (sin80*)=80* true?

A: We know the basic relations      cos(cos-1x)=x Because cos and cos-1 are opposite functions,…

Q: Rewrite cos ( x in terms of sin(æ) and cos(x). 4 -

A: we know that cos(a-b)=cosa cosb+sina sinb

Q: determine the value of sin^2 x + cos^2 x for x =10 degrees

A: Given x= 10 degrees By trigonometric formula we know that , sin2(x)+cos2(x)=1 where x∈-∞,∞

Q: Prove the identity. TT COS +0+ -sin 0

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Q: 16. Find the exact value of: π a) sin¹(tan(- =)) 3 √₂ 2 b) sin(cos-1(-

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Q: Find sin(2x), cos(2x), and tan(2x) from the given information. cos(x) = , csc(x) < 0 %3D

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Q: Prove that cos(sin-x) = /I– x².

A: Given: sin-1x=cos-11-x2

Q: The value of (cos x sin xdx =

A: It is definite integration problem.

Q: 33. Use addition formulas and the values of sin 0 and cos 0 for 0 = to compute sin 12 and cos…

A: Given: sin7π12, cos7π12 We know that sinA+B=sinAcosB+cosAsinB…

Q: 1- cos 0 1+ cos 0 sin 0

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Q: Verify the identity : cos (x - 5π/4) = - √2(cos x + sin x)/2.

A: Consider the given expression as, cosx-5π4

Q: Verify that the equation is an identity. 2 cos x 1. cos X 1. 1+cos x 2.

A: It is trigonometric verification.