Choose the correct option and Justify your choice.
(sec A + tan A) (1 - sin A) =
(A) sec A (B) sin A (C) cosec A (D) cos A

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Solution

space left parenthesis Sec space straight A plus space tan space straight A right parenthesis space left parenthesis 1 minus sinA right parenthesis space space space space space space space space space space space space space space space space space equals space open parentheses 1 over cosA plus sinA over cosA close parentheses space left parenthesis 1 minus sinA right parenthesis space space space space space space space space space space space space space space space space space equals space fraction numerator left parenthesis 1 plus sinA right parenthesis space over denominator cos space straight A end fraction left parenthesis 1 minus sinA right parenthesis space space space space space space space space space space space space space space space space space space equals space fraction numerator 1 minus sin squared straight A over denominator cosA end fraction space equals space fraction numerator cos squared straight A over denominator cos space straight A end fraction equals space cosA

Hence, correct option is (D)

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