Question

$(\sec \theta + \tan \theta)(1 - \sin \theta)$ is equal to:

• A. $\sec \theta$
• B. $\sin \theta$
• C. $\cosec \theta$
• D. $\cos \theta$

Answer 1

The Correct Option is D

Simplify the expression:
\[(\sec \theta + \tan \theta)(1 - \sin \theta)\]
Substitute $\sec \theta = \frac{1}{\cos \theta}$ and $\tan \theta = \frac{\sin \theta}{\cos \theta}$:
\[\frac{1 + \sin \theta}{\cos \theta}(1 - \sin \theta)\]
Simplify further using the identity:
\[\frac{(1 + \sin \theta)(1 - \sin \theta)}{\cos \theta} = \frac{1 - \sin^2 \theta}{\cos \theta}\]
\[= \frac{\cos^2 \theta}{\cos \theta} = \cos \theta\]