Question

Fill in the blank

$\sec A(1-\sin A)(\sec A+\tan A)=$ _____

Answer 1

Given : $\sec A(1-\sin A)(\sec A+\tan A)$

$\frac{1}{\cos A}(1-\sin A)(\frac{1}{\cos A}+\frac{\sin A}{\cos A})$...................$(\because secA=\frac{1}{cosA})$

$\left(\frac{1-\sin A}{\cos A}\right)\left(\frac{1+\sin A}{\cos A}\right)$

$\frac{1-{\sin }^{2}A}{{\cos }^{2}A}$

As, $1-{\sin }^{2}A={\cos }^{2}A$

$\frac{{\cos }^{2}A}{{\cos }^{2}A}$ $=1$