1.

\(\frac{sec A(sec A + tan A )(1 - sin A)}{(cosec^2 A - 1) sin^2 A}\) is equal to:1. cos2 A2. sec2 A3. cot A4. cos A

Answer» Correct Answer - Option 2 : sec2 A

Given :

\(\frac{sec A(sec A + tan A )(1 - sin A)}{(cosec^2 A - 1) sin^2 A}\)

Concept used :

sec a = 1/(cos a)

tan a = (sin a)/(cos a)

Solution :

\(\frac{sec A(sec A + tan A )(1 - sin A)}{(cosec^2 A - 1) sin^2 A}\)

\( = \left[ {\frac{1}{{cosA}}\left( {\frac{1}{{cosA}} + \frac{{sinA}}{{cosA}}} \right)\left( {1 - sinA} \right)} \right]/[(1/{\sin ^2}A) - 1]\;{\rm{sin}}{\;^2}A\;\)

\( = [1/cosA(1 + sinA)(1 - sinA)]/[((1 - si{n^2}A)/si{n^2}A){\rm{ \times }}si{n^2}A]\)

\( = se{c^2}A(1 - si{n^2}A)/((1 - si{n^2}A))\)

= sec2 A


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