If $cotθ space equals space 15 over 8 comma$ then evaluate

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Solution

fraction numerator left parenthesis 2 plus 2 sinθ right parenthesis thin space left parenthesis 1 minus sinθ right parenthesis over denominator left parenthesis 1 plus cosθ right parenthesis thin space left parenthesis 2 minus 2 cosθ right parenthesis end fraction equals space fraction numerator 2 left parenthesis 1 plus sinθ right parenthesis thin space left parenthesis 1 minus sinθ right parenthesis over denominator 2 left parenthesis 1 plus cosθ right parenthesis space left parenthesis 1 minus cosθ right parenthesis end fraction equals space fraction numerator 1 minus sin squared straight theta over denominator 1 minus cos squared straight theta end fraction space equals space fraction numerator cos squared straight theta over denominator sin squared straight theta end fraction space equals space cot squared straight theta equals space open parentheses 15 over 8 close parentheses squared space equals space 225 over 64 space Ans. space

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