Prove the following: [cos (π + x) cos (-x)] / [sin (π - x) cos (π/2 + x)] = cot²x

Solution:

LHS :

 [cos (π + x) cos (-x)] / [sin (π - x) cos (π/2 + x)]

= [(-cos x) × (cos x)] / [ (sin x) × (-sin x)]   

[Since cos (π + x) = -cos x, cos(-x) = cos x, cos (π/2 + x) = -sin x, and sin (π-x) = sinx] 

= -cos²x / -sin²x

= cot²x 

 [because cot x = cos x / sin x]

= RHS

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.3 Question 8

Prove the following: [cos (π + x) cos (-x)] / [sin (π - x) cos (π/2 + x)] = cot²x

Summary:

We got, [cos (π + x) cos (-x)] / [sin (π - x) cos (π/2 + x)] = cot²x. Hence Proved