Question

prove the following. cosA/1-sinA + cosA/1+sinA = 2secA​

Answer 1

Step-by-step explanation:

$\\ \rm \text{ prove \: the \: following :- }\frac{cosA}{1-sinA }+ \frac{cosA}{1+sinA} = 2secA$

$\[ \begin{array}{l} \displaystyle \rm \text { LHS }=\frac{\cos A }{1-\sin A }+\frac{\cos A }{1+\sin A }= \\ \\ \displaystyle \rm\frac{\cos A (1+\sin A +1-\sin A )}{\left(1-\sin ^{2} A \right)}=\frac{2 \cos A }{\cos ^{2} A } \\\\ \displaystyle \rm =\frac{2}{\cos A } \\\\ \red{\displaystyle \rm =2 \sec A } \rm= RHS \\ \\ \text{Hence Proved.}\end{array} \]$