Inverse Trigonometric Functions
Equations
Premium Question
Grade 12
Question:
If $2 \tan^{-1}(\cos \theta) = \tan^{-1}(2 \csc \theta)$, then $\theta$ equals:
(1) $\frac{\pi}{6}$
(2) $\frac{\pi}{4}$
(3) $\frac{\pi}{3}$
(4) $\frac{\pi}{2}$
Step-by-Step Solution
Key Concept: Apply $2 \tan^{-1}(a) = \tan^{-1}(2a/(1 - a^2))$ to the left side. The resulting equation simplifies to a single trig identity.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)