Question

The value of $\tan^{-1}\left(\frac{\cos x-\sqrt{3}\sin x}{\sqrt{3}\cos x+\sin x}\right)$ , where $0<x<\frac{\pi}{2}$ is

• A. $\frac{\pi}{6}-x$
• B. $\frac{\pi}{4}-x$
• C. $\frac{\pi}{3}-x$
• D. $\frac{\pi}{2}-x$
• E. $\pi-x$

Hint:

Logic Tip: Whenever you see an expression of the form $\frac{a\cos x - b\sin x}{b\cos x + a\sin x}$ inside an inverse tangent, immediately divide everything by $b\cos x$ (the bottom-left term) to create the $1 + \dots$ structure needed for the $\tan(A-B)$ formula.

Answer 1

The Correct Option is A