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Question
Prove that:
(sec A – tan A)2 (1 + sin A) = (1 – sin A)
Sum
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Solution
L.H.S. = (sec A – tan A)2 (1 + sin A)
= `[1/cosA - sinA/cosA]^2 (1 + sinA)`
= `[(1 - sinA)/cosA]^2 (1 + sinA)`
= `((1 - sinA)^2(1 + sinA))/(cos^2A)`
= `((1 - sinA)^2(1 + sinA))/(1 - sin^2A)`
= `((1 - sinA)^2(1 + sinA))/((1 - sinA)(1 + sinA))`
= 1 – sin A = R.H.S.
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