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Some Applications Of Trigonometry

Question

Prove the following identities:
$fraction numerator sinθ minus cosθ plus 1 over denominator sinθ plus cosθ minus 1 end fraction space equals space fraction numerator 1 over denominator secθ minus tanθ end fraction.$

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Solution

fraction numerator sinθ minus cosθ plus 1 over denominator sinθ plus cosθ minus 1 end fraction equals fraction numerator 1 over denominator secθ minus tanθ end fraction

Hence, L.H.S. = R.H.S.