Prove the following identities: 11+cosA+11-cosA=2cosec2A

Prove the following identities:

`1/(1 + cosA) + 1/(1 - cosA) = 2cosec^2A`

Sum

L.H.S. = `1/(1+cosA)+1/(1-cosA)`

= `(1 - cosA + 1 + cosA)/((1 + cosA)(1 - cosA))`

= `2/(1 - cos^2A)` ...(∵ 1 – cos² A = sin² A)

= `2/(sin^2A)`

= 2 cosec² A = R.H.S.

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Prove the following trigonometric identities. `(1 - cos A)/(1 + cos A) = (cot A - cosec A)^2`

Prove the following identities:

`sqrt((1 + sinA)/(1 - sinA)) = sec A + tan A`

Prove that:

`cosA/(1 + sinA) = secA - tanA`

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