Question

The value of $sin\left(co{t}^{-1}\right(cos\left(ta{n}^{-1}x\right)\left)\right)$ is equal to

• A. $\sqrt{\frac{x^2+1}{x^2+2}}$
• B. $\sqrt{\frac{x+2}{x^2+1}}$
• C. $\sqrt{\frac{x^2-1}{x^2+2}}$
• D. $\sqrt{\frac{x^2+2}{x^2+1}}$

Answer 1

The correct option is A $\sqrt{\frac{x^2+1}{x^2+2}}$

$sin\left(si{n}^{-1}\left(\frac{1}{\sqrt{1+co{s}^2\theta }}\right)\right)=\frac{1}{\sqrt{1+co{s}^2\theta }}=\frac{sec\theta }{\sqrt{1+se{c}^2\theta }}=\frac{\sqrt{1+x^2}}{\sqrt{2+x^2}}$