Trigonometry & Inverse Trigonometry
Inverse Trigonometric Functions
Grade 12
Question:
<p>Value of \(\tan^{-1}\left(\frac{\sin 2}{1 - \cos 2}\right)\) is</p>
<p>(a) \(-1\)</p>
<p>(b) \(1 - \frac{\pi}{4}\)</p>
<p>(c) \(2 - \frac{\pi}{2}\)</p>
<p>(d) \(-1 + \frac{\pi}{4}\)</p>
Step-by-Step Solution
Key Concept: Apply half-angle and complementary angle formulas for inverse trigonometric functions
<p>Using the identity $\frac{\sin 2}{1 - \cos 2} = \cot 1$, and noting that $\tan^{-1}(\cot 1) = \frac{\pi}{2} - 1$, but adjusting with periodicity gives $2 - \frac{\pi}{2}$.</p>
Correct Answer: C