Question

$\frac{\pi}{2} \le \theta \le \frac{3\pi}{4}$ then $\cos^{-1}(\frac{5}{13} \sin \theta + \frac{12}{13} \cos \theta) =$

• A. $\theta - \tan^{-1}(\frac{4}{3})$
• B. $\theta + \tan^{-1}(\frac{5}{12})$
• C. $\theta + \tan^{-1}(\frac{4}{5})$
• D. $\theta - \tan^{-1}(\frac{5}{12})$

Hint:

Always identify the coefficients as $\sin$ and $\cos$ of a common angle to simplify inverse trigonometric expressions.

Answer 1

The Correct Option is D