Question

Find the value of $\tan \theta \sin \theta +\cos \theta$

• A. 1
• B. $\text{cosec}\theta$
• C. $\sin \theta$
• D. $\sec \theta$

Answer 1

The correct option is D $\sec \theta$

$\tan \theta sin\theta +\cos \theta =\frac{\sin \theta }{\cos \theta }\cdot \sin \theta +\cos \theta$
$=\frac{{\sin }^2\theta }{\cos \theta }+\cos \theta =\frac{{\sin }^2\theta +{\cos }^2\theta }{\cos \theta }$
$=\frac{1}{\cos \theta }=\sec \theta$