Question

If x=cosecA+cosA and y=cosecA-cosA then prove that (2/x+y) the whole square +(x-y/2) the whole square=1

Answer 1

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Answer 2

$x = \csc( \alpha ) + \cos( \alpha ) \\ y = \csc( \alpha ) - \cos( \alpha ) \\ so \\ value \: of \: \\ x + y = 2 \csc( \alpha ) .....(1) \\ x - y = 2 \cos( \alpha ) ......(2) \\ now \: \\ ( \frac{2}{x + y} ) {}^{2} + ( \frac{x - y}{2} ) {}^{2} \\ = ( \frac{2}{2 \csc( \alpha ) } ) {}^{2} + (\frac{2 \cos( \alpha ) }{2} ) {}^{2} \\ = {sin}^{2} \alpha + {cos}^{2} \alpha = 1$
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