Question

Choose the correct option. Justify your choice.
$(\sec A+\tan A)(1-\sin A)=$?

• A. $\sec A$
• B. $\sin A$
• C. $cosecA$
• D. $\cos A$

Answer 1

The correct option is D $\cos A$

$(Weknowthat\frac{\sin \theta }{\cos \theta }=\tan \theta$ & $\sec \theta =\frac{1}{\cos \theta })$

So,

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

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

$=\frac{1-{\sin }^{2}A}{\cos A}\left(\right(a-b\left)\right(a+b)=a^2-b^2)$

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

$=\cos A$

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