Prove the identity. tan(x) − tan(y) 1 − tan(x) tan(y) =  sin(x − y) cos(x + y)

Q: tan (5) dx sin (x) Evaluate a. tan () + C O b. cot () + C Oc.2 cot (풍) + C o d. 2tan(풍) +C

A: Option (a) is correct.

Q: If sin(x + y) – sin(x – y) = 2f(x) sin y, then f(x) is equal to C. tan x D. cos? x A. sin c B. cos x

A: Trigonometric functions are also known as circular functions. They can be defined as the functions…

Q: cos(2 tan−1(x))

A: Given,

Q: cos( – x) + tan( – x)sin( – 2)

A:

Q: 3r cos(x) 1. Evaluate dx V1+ sin(x)

A:

Q: sin( – x) = cos x = COS X

A: Given: To prove that sin(π2-x)=cos x

Q: cos (E) U4+ tan(t)

A:

Q: sin(cos (2x)), where 0<x<

A:

Q: Verify. a. (2 tan x ) / (1 + tan2 x) = sin(2x) b.  1 / (1 − sin θ) + 1 / (1 + sin θ) = 2 sec2 θ c. 1…

A: Part a)Given:

Q: cos(sin−1(x) − tan−1(y))

A: Important points:  cos(A + B) = cos A. cos B - sin A. sin B sin(sin-1x) = xcos(cos-1x) =…

Q: Verify. esc (x) [I-cos(2x)] = 2 sin (x) SC

A:

Q: Differentiate. H(t) = cos2(t)

A: answer = -2sin2t   explanation is given in the below step

Q: n/4 1+sin x 7. So cos (x)

A: We will solve the following.

Q: Find the exact value of cos(4x) if tan(x) = -2,2 <y<T.

A:

Q: 1. Evaluate dx sec2 x (a) Ja(x+ 4) (b) A. dx V1- tan?x VT(x + 4)

A:

Q: (−x)cos(−x)+sin(−x)=−1f(x)

A:

Q: Evaluate sin (x) cos“(x) dx.

A: ∫ππsin6x cos4x dx

Q: Find x cos(x)-sin(x) = 0

A:

Q: | cos(x) sin(2x) dæ

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.