Question

Cos A/ 1+sin A +1 +sin A /Cos A =2secA​

Answer 1

Answer:

In This Question we have to prove that :-

$\large{\frac{cosA}{1 + sin A } + \frac{1 + sin A}{cos A } = 2secA}$

Now,

LHS:-)

$\large{\frac{cosA}{1 + sin A } + \frac{1 + sin A}{cos A } } \\ \\ = \frac{ {(cosA)}^{2} + {(1 + sin A) }^{2} }{(1 + sinA)(cos A) } \\ \\ = \large{ \frac{ {cos}^{2}A + 1 + {sin}^{2}A + 2sin A}{(1 + sin A )(cosA) } } \\ \\ = \large{ \frac{2 + 2sin A}{(1 + sinA)(cos A)} } \\ \\ = \large \frac{{2( \cancel{1 + sinA})}}{ ( \cancel{1 + sinA})(cos A) } \\ \\ = \large \frac{2 }{cos A} \\ \\ = 2secA$

HENCE,

$\bold{ \huge{ \boxed{ \boxed{ LHS=RHS }}}}$