Question

cosA/(1-tanA) - sin^2A/(coaA-sinA) = cosA+sinA prove it
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Answer 1

Step-by-step explanation:

$\implies \sf{\dfrac{cosA}{1-tanA} -\dfrac{sin^2A }{cosA - sinA} }$

$\sf{\implies \dfrac{cosA}{1-\frac{sinA}{cosA}} - \dfrac{sin^2}{cosA-sinA}}$

$\sf{\implies \dfrac{cosA}{\frac{cosA-sinA}{cosA}} - \dfrac{sin^2}{cosA-sinA}}$

$\sf{\implies \dfrac{cos^2A}{cosA-sinA} - \dfrac{sin^2}{cosA-sinA}}$

$\sf{\implies \dfrac{cos^2A-sin^2A}{cosA-sinA}}$

$\sf{\implies \dfrac{(cosA+sinA)(cosA-sinA)}{cosA-sinA}}$

$\implies \sf{cosA + sinA}$