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The value of $$[\frac{cos^2A(sinA + cosA)}{cosec^2A(sinA-cosA)} + \frac{sin^2A(sinA - cos A)}{sec^2A(sinA + cos A)}]$$$$(sec^2A - cosec^2 A)$$
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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