Question

If $f ( x )= x ^{11}+ x ^9- x ^7+ x ^3+1$ and $f \left(\sin ^{-1}(\sin 8)\right)=\alpha$, then $f \left(\tan ^{-1}(\tan 8)\right)$ is equal to

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

Answer 1

Answer: (D)

$ \Theta \sin ^{-1}(\sin 8)=\sin ^{-1}(\sin (3 \pi-8))=3 \pi-8 $
$\text { and } \tan ^{-1}(\tan 8)=\tan ^{-1}(\tan (8-3 \pi))=8-3 \pi $
$\therefore f ( x )+ f (- x )=2 $
$\therefore f (3 \pi-8)+ f (8-3 \pi)=2$
$\Rightarrow f (8-3 \pi)= f \left(\tan ^{-1}(\tan 8)\right)=2-\alpha .$