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Please help me solve this question on trigonometry ​

Answer»

Step-by-step EXPLANATION:

LET A= α,

Then,

x = \cot( \alpha ) + \cos( \alpha ) \: \: and \: \: y = \cot( \alpha ) - \cos( \alpha )

Now,

{ (\frac{x - y}{x + y}) }^{2} + { (\frac{x - y}{2} )}^{2}

= (\frac{ \cot( \alpha ) + \cos( \alpha ) - \cot( \alpha ) + \cos( \alpha ) }{ \cot( \alpha ) + \cos( \alpha ) + \cot( \alpha ) - \cos( \alpha ) } )^{2} + { (\frac{ \cot( \alpha ) + \cos( \alpha ) - \cot( \alpha ) + \cos( \alpha ) }{2} })^{2}

= ({ \frac{2 \cos( \alpha ) }{2 \cot( \alpha ) } })^{2} + ({ \frac{2 \cos( \alpha ) }{2} })^{2}

= \frac{ \cos^{2} ( \alpha ) }{ \cot ^{2} ( \alpha ) } + \cos^{2} ( \alpha )

= \sin^{2} ( \alpha ) + \cos^{2} ( \alpha )

= 1

HENCE PROVED


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