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1. The value of $$[\frac{cos^2A(sinA + cosA)}{cosec^2A(sinA-cosA)} + \frac{sin^2A(sinA - cos A)}{sec^2A(sinA + cos A)}]$$$$(sec^2A - cosec^2 A)$$
(A): 1
(B): 3
(C): 2
(D): 4
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By: anil on 05 May 2019 02.58 pm
Expression : $$[frac{cos^2A(sinA + cosA)}{cosec^2A(sinA-cosA)} + frac{sin^2A(sinA - cos A)}{sec^2A(sinA + cos A)}]$$$$(sec^2A - cosec^2 A)$$ = $$[cos^2A sin^2A frac{(sinA + cosA)}{(sinA - cosA)} + cos^2A sin^2A frac{(sinA - cosA)}{(sinA + cosA)}] (sec^2A - cosec^2A)$$ = $$(cos^2A sin^2A) [frac{(sinA + cosA)^2 + (sinA - cosA)^2}{(sinA - cosA)(sinA + cosA)}] (frac{1}{cos^2A} - frac{1}{sin^2A})$$ = $$(cos^2A sin^2A) (frac{sin^2A - cos^2A}{cos^2A sin^2A}) [frac{(sin^2A + cos^2A + 2 sinA cosA) + (sin^2A + cos^2A - 2 sinA cosA)}{sin^2A - cos^2A}]$$ = $$1 + 2 sinA cosA + 1 - 2 sinA cosA$$ = $$2$$
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SSC CGL 2013 Tier 1 19 May Evening II
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