Question

If $\sin \theta =\cos \theta$;

find value of $2\tan \theta +{\cos }^2\theta$.

• A. $-\frac{5}{2}$
• B. $\frac{5}{8}$
• C. $\frac{3}{2}$
• D. $\frac{5}{2}$

Answer 1

The correct option is D $\frac{5}{2}$

$If$ $\sin \theta$ $=$ $\cos \theta$

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

$=$ $2$ $+$ ${\cos }^2\theta$

$=$ $2$ $+$ $\frac{1}{{\sec }^2\theta }$

$=$ $2$ $+$ $\frac{1}{1+{\tan }^2\theta }$

$=$ $2$ $+$ $\frac{1}{1+1}$

$=$ $2$ $+$ $\frac{1}{2}$

$=$ $\frac{5}{2}$