Question Number 30823 by drishtantsingh315 last updated on 26/Feb/18
Answered by math1967 last updated on 27/Feb/18
![Cos[tan^(−1) {sin (cot^(−1) x)}] cos [tan^(−1) {sin (sin^(−1) (1/( (√(1+x^2 )) )))}] cos [tan^(−1) {(1/( (√(1+x^2 )) ))}] cos [cos^(−1) {(((√(1+x^2 )) )/( (√(1+1+x^2 ))))}] (√((1+x^2 )/(2+x^2 )))](https://www.tinkutara.com/question/Q30853.png)
$${Cos}\left[\mathrm{tan}^{−\mathrm{1}} \left\{\mathrm{sin}\:\left(\mathrm{cot}^{−\mathrm{1}} {x}\right)\right\}\right] \\ $$$$\mathrm{cos}\:\left[\mathrm{tan}^{−\mathrm{1}} \left\{\mathrm{sin}\:\left(\mathrm{sin}^{−\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:}\right)\right\}\right] \\ $$$$\mathrm{cos}\:\left[\mathrm{tan}^{−\mathrm{1}} \left\{\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:}\right\}\right] \\ $$$$\mathrm{cos}\:\left[\mathrm{cos}^{−\mathrm{1}} \left\{\frac{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} \:}\:}{\:\sqrt{\mathrm{1}+\mathrm{1}+{x}^{\mathrm{2}} \:}}\right\}\right] \\ $$$$\sqrt{\frac{\mathrm{1}+{x}^{\mathrm{2}} }{\mathrm{2}+{x}^{\mathrm{2}} }} \\ $$