Question

If \(x\in\left(0,\frac{1}{\sqrt2}\right)\), then \[ \cot\left[\cos^{-1}\{\tan(\sin^{-1}x)\}\right]= \]

• A. \(\sqrt{\frac{1-x^2}{1-2x^2}}\)
• B. \(\frac{x}{\sqrt{1-2x^2}}\)
• C. \(\sqrt{\frac{1-2x^2}{1-x^2}}\)
• D. \(\frac{\sqrt{1-2x^2}}{x}\) \bigskip

Hint:

Convert inverse trig into triangle ratios instead of direct identities.

Answer 1

The Correct Option is C