#### Question

Prove the following identities, where the angles involved are acute angles for which the expressions are defined

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

#### Solution

L.H.S

`= (cosec θ – cot θ)^2`

`=(1/sintheta - costheta/sintheta)^2`

`=(1-costheta)^2/(sin theta)^2 = (1-cos theta)^2/(sin^2theta)`

`= (1-costheta)^2/(1-cos^2 theta) = (1-costheta)^2/((1-costheta)(1+cos theta)) = (1-cos theta)/(1+costheta)`

= R.H.S

Is there an error in this question or solution?

Solution Prove the Following Identities, Where the Angles Involved Are Acute Angles for Which the Expressions Are Defined Concept: Trigonometric Identities.