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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^2 theta)`
= `(1-cos theta)^2/(1-cos^2theta)`
= `((1-costheta)(1-costheta))/((1-costheta)(1+cos theta)) `
= `(1-cos theta)/(1+costheta)`
= R.H.S
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