Question

Prove that Cosec²+sec²=Cosec².sec²

Answer 1

$Cosec^{2}A+Sec^{2}A = \frac{1}{Sin^{2}A} + \frac{1}{Cos^{2}A}$
=$\frac{ Cos^{2}A + Sin^{2}A}{Cos^{2}ASin^{2}A}$
=$\frac{1}{Cos^{2}A.Sin^{2} }$ $(where Sin^{2}A+Cos^{2}A = 1)$
=$\frac{1}{Cos^{2}A } . \frac{1}{Sin^{2}A }$
=$Sec^{2}A.Cosec^{2}A$

Answer 2

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