# Prove the Following Trigonometric Identities. (1 + Cos Theta - Sin^2 Theta)/(Sin Theta (1 + Cos Theta)) = Cot Theta - Mathematics

Prove the following trigonometric identities.

(1 + cos theta - sin^2 theta)/(sin theta (1 + cos theta)) = cot theta

#### Solution

In the given question, we need to prove (1 + cos theta - sin^2 theta)/(sin theta (1 + cos theta)) = cot theta

Using the property  sin^2 theta + cot^2 theta = 1 we get

So

(1 + cos theta - sin^2 theta)/(sin theta (1 +  cos theta))

= (1 + cos theta - (1 - cos^2 theta))/(sin theta (1 + cos theta)

= (cos theta + cos^2 theta)/(sin theta (1 + cos theta))

Solving further, we get

(cos theta + cos^2 theta)/(sin(1 + cos theta)) = (cos theta (1 + cos theta))/(sin theta(1 + cos theta))

= cos theta/sin theta

= cot theta

Hence proved.

Concept: Trigonometric Identities
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Chapter 11: Trigonometric Identities - Exercise 11.1 [Page 45]

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 11 Trigonometric Identities
Exercise 11.1 | Q 53 | Page 45

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