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# Prove the following: [cos (π + x) cos (-x)] / [sin (π - x) cos (π/2 + x)] = cot^{2}x

**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]

= -cos^{2}x / -sin^{2}x

= cot^{2}x

[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)] = cot^{2}x

**Summary:**

We got, [cos (π + x) cos (-x)] / [sin (π - x) cos (π/2 + x)] = cot^{2}x. Hence Proved

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