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Prove the Following Trigonometric Identities. (1 + Cos Theta + Sin Theta)/(1 + Cos Theta - Sin Theta) = (1 + Sin Theta)/Cos Theta - CBSE Class 10 - Mathematics

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Question

Prove the following trigonometric identities.

`(1 + cos theta + sin theta)/(1 + cos theta - sin theta) = (1 + sin theta)/cos theta`

Solution

We have to prove the following identity

`(1 + cos theta + sin theta)/(1 + cos theta - sin theta) = (1 + sin theta)/cos theta`

Consider the LHS = `(1 + cos theta + sin theta)/(1 + cos theta - sin theta)`

`= ((1 + cos theta + sin theta)/(1 + cos theta - sin theta))((1 + cos theta + sin theta)/(1 + cos theta + sin theta))`

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

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

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

`= (1 + sin theta)/cos theta`

= RHS

Hence proved

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