Question

If \(|x|\ge1\), then \(\tan\!\left[\dfrac{2}{3}\big(\tan^{-1}x+\cot^{-1}x\big)\right]=\) ?

• A. \(\dfrac{12}{\sqrt3}\)
• B. \(\sqrt3\)
• C. \(0\)
• D. \(1\)

Hint:

Once the inside is a fixed angle, evaluate the outer trig directly.

Answer 1

The Correct Option is B

Using \(\tan^{-1}x+\cot^{-1}x=\dfrac{\pi}{2}\), \[ \tan\!\left[\frac{2}{3}\cdot\frac{\pi}{2}\right]=\tan\!\left(\frac{\pi}{3}\right)=\sqrt3. \]