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Question
Prove that `(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`
Solution
`(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`
L.H.S. `(cot A - cos A)/(cot A + cos A)`
= `(cos A/sin A - cos A)/(cos A/sin A + cos A)`
= `(cos A(1/sinA - 1))/(cos A(1/sin A + 1))`
= `(1/sin A - 1)/(1/sin A + 1)`
= `(1 - sin A)/(1 + sin A)`
= `(1 - sin A)/(1 + sin A) xx (1 + sin A)/(1 + sin A)`
= `(1 - sin^2 A)/(1 + sin A)^2`
= `cos^2 A/(1 + sin A)^2`
= R.H.S.
Hence Proved.
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