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

Prove the following trigonometric identities.

1 + cot^2 theta/(1 + cosec theta) = cosec theta

#### Solution

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

Using cot theta = cos theta/sin theta and cosec theta = 1/sin theta We get

1 + cot^2 theta/(1 +  cosec theta) = (1 = cosec theta +  cot^2 theta)/(1 + cosec theta)

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

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

Further, using the property sin^2 theta + cos^2 theta = 1

We get

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

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

= 1/sin theta

= cosec theta

Hence proved.

Is there an error in this question or solution?
Chapter 11: Trigonometric Identities - Exercise 11.1 [Page 45]

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 11 Trigonometric Identities
Exercise 11.1 | Q 51 | Page 45
RD Sharma Class 10 Maths
Chapter 11 Trigonometric Identities
Exercise 11.1 | Q 51 | Page 45

Share