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# Prove the Following Trigonometric Identities. (Cos Theta)/(Cosec Theta + 1) + (Cos Theta)/(Cosec Theta - 1) = 2 Tan Theta - CBSE Class 10 - Mathematics

#### Question

Prove the following trigonometric identities.

(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta

#### Solution

In the given question, we need to prove (cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta

Using the identity a^2 - b^2  = (a + b)(a - b)

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

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

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

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

= 2 sin theta/cos theta

= 2 tan theta

Hence proved.

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Solution Prove the Following Trigonometric Identities. (Cos Theta)/(Cosec Theta + 1) + (Cos Theta)/(Cosec Theta - 1) = 2 Tan Theta Concept: Trigonometric Identities.
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