MCQ
(sec A + tan A) (1 – sin A) =
- Asec A
- Bsin A
- Ccosec A
- ✓cos A
✓
Answer
Correct option: D.
cos A
(d) cos A
$\begin{array}{l}(\sec A+\tan A)(1-\sin A) \\
=\left(\frac{1}{\cos A}+\frac{\sin A}{\cos A}\right)(1-\sin A) \\
=\left(\frac{1+\sin A}{\cos A}\right)(1-\sin A) \\
=\frac{1-\sin ^2 A}{\cos A} \\
=\frac{\cos ^2 A}{\cos A} \\
=\cos A\end{array}$
Hence, alternative $\cos A$ is correct.
$\begin{array}{l}(\sec A+\tan A)(1-\sin A) \\
=\left(\frac{1}{\cos A}+\frac{\sin A}{\cos A}\right)(1-\sin A) \\
=\left(\frac{1+\sin A}{\cos A}\right)(1-\sin A) \\
=\frac{1-\sin ^2 A}{\cos A} \\
=\frac{\cos ^2 A}{\cos A} \\
=\cos A\end{array}$
Hence, alternative $\cos A$ is correct.
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