Question

Trigonometry Ka question​

Answer 1

Answer:

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Step-by-step explanation:

FROM L.H.S-------

$\frac{cot^2A(sec-1)}{1+sinA}= sec^2(\frac{1-sinA}{1+secA} )$

=> $\frac{cot^2A (\frac{1}{cosA} -   1)}{1+sinA}=$

=> $\frac{\frac{cos^2A}{sin^2A}(\frac{1-cosA}{cosA} ) }{1+sinA}$

after cutting we obtain

$\frac{\frac{cosA(1-cosA)}{sin^2A} }{1+sinA}$

$\frac{cosA(1-cosA)(1+sinA)}{sin^2a}$$\frac{cosA(1-cosA)(1+sinA)}{(1+cosA)(1-cosA)}$$cos(\frac{1+sinA}{1+cosA} )=\\from RHS\\sec^2A(\frac{1+sinA}{1+secA} )\\= \frac{1}{cos^2A}* \frac{1+sinA}{1+\frac{1}{cosA} }\\\\\frac{1}{cos^2A}*\frac{1-sinA}{\frac{cosA+1}{cosA} } \\   1/cosA * 1+sinA/1+cosA\\hence proove it$