If a= ^ -1 ( (5)) and b= ^ -1 ( (5)), then a^2+b^2 is equal to - Vidyadip

MCQ

If $a=\sin ^{-1}(\sin (5))$ and $b=\cos ^{-1}(\cos (5))$, then $a^2+b^2$ is equal to

A
$4 \pi^2+25$
✓
$8 \pi^2-40 \pi+50$
C
$4 \pi^2-20 \pi+50$
D
$25$

✓

Answer

Correct option: B.

$8 \pi^2-40 \pi+50$

b
$a=\sin ^{-1}(\sin 5)=5-2 \pi $

$\text { and } b=\cos ^{-1}(\cos 5)=2 \pi-5 $

$\therefore a^2+b^2=(5-2 \pi)^2+(2 \pi-5)^2 $

$=8 \pi^2-40 \pi+50$

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