Question

$sin\left[co{t}^{-1}\left\{cos\left(ta{n}^{-1}x\right)\right\}\right]=$

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

Answer 1

Answer: (A)

$sin\left[co{t}^{-1}\left\{cos\left(ta{n}^{-1}x\right)\right\}\right]$
$=sin\left[co{t}^{-1}\left\{cos\left(co{s}^{-1}\frac{1}{\sqrt{1+x^2}}\right)\right\}\right]$
$=sin\left[co{t}^{-1}\frac{1}{\sqrt{1+x^2}}\right]$
$=sin\left[si{n}^{-1}\frac{\sqrt{1+x^2}}{\sqrt{2+x^2}}\right]$
$=\frac{\sqrt{1+x^2}}{\sqrt{2+x^2}}=\sqrt{\frac{x^2+1}{x^2+2}}$