Question

The value of $(\sec A+\tan A)(1-\sin A)$ is equal to :

• A. $\sec A$
• B. $\sin A$
• C. $\text{cosec}A$
• D. $\cos A$.

Answer 1

The correct option is D $\cos A$.

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

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

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

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

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

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

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

Hence, the answer is $\cos A.$