Question

If $f\left(x\right)=x^{11}+x^9-x^7+x^3+1$ and $f\left({sin}^{-1}\right(sin8\left)\right)=\alpha ,\alpha$ is a constant, then $f\left({tan}^{-1}\right(tan8\left)\right)$ is equal to

• A. $\alpha$
• B. $\alpha -2$
• C. $\alpha +2$
• D. $2-\alpha$

Answer 1

The correct option is A $\alpha$

Given,

$f\left({\sin }^{-1}\sin 8\right)=\alpha$

$\Rightarrow f\left(8\right)=\alpha$

$\therefore f\left({\tan }^{-1}\tan 8\right)$

$=f\left(8\right)$

$=\alpha$