Prove the following identity:
$left parenthesis secA minus tanA right parenthesis squared space left parenthesis 1 plus sinA right parenthesis space equals space 1 minus space sinA.$

Solution

L.H.S. = $left parenthesis secA minus tanA right parenthesis squared space left parenthesis 1 plus sinA right parenthesis$
$space equals space open parentheses 1 over cosA minus sinA over cosA close parentheses squared space left parenthesis 1 plus sinA right parenthesis equals space open parentheses fraction numerator 1 minus sinA over denominator cosA end fraction close parentheses squared space left parenthesis 1 plus sinA right parenthesis space equals space fraction numerator left parenthesis 1 minus sinA right parenthesis squared over denominator cos squared straight A end fraction left parenthesis 1 plus sinA right parenthesis equals space fraction numerator left parenthesis 1 minus sinA right parenthesis squared over denominator 1 minus sin squared straight A end fraction left parenthesis 1 plus sinA right parenthesis space equals space fraction numerator left parenthesis 1 minus sinA right parenthesis squared space left parenthesis 1 plus sinA right parenthesis over denominator left parenthesis 1 minus sinA right parenthesis thin space left parenthesis 1 plus sinA right parenthesis end fraction space equals space 1 minus sinA space equals space straight R. straight H. straight S.$

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Some Applications Of Trigonometry

Prove the following identity:
$left parenthesis secA minus tanA right parenthesis squared space left parenthesis 1 plus sinA right parenthesis space equals space 1 minus space sinA.$

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