Inverse Trigonometric Functions Question 4
Question 4 - 2024 (31 Jan Shift 2)
If $a=\sin ^{-1}(\sin (5))$ and $b=\cos ^{-1}(\cos (5))$, then $a^{2}+b^{2}$ is equal to
(1) $4 \pi^{2}+25$
(2) $8 \pi^{2}-40 \pi+50$
(3) $4 \pi^{2}-20 \pi+50$
(4) 25
Show answer
Answer (2)
Solution
$a=\sin ^{-1}(\sin 5)=5-2 \pi$
and $b=\cos ^{-1}(\cos 5)=2 \pi-5$
$\therefore a^{2}+b^{2}=(5-2 \pi)^{2}+(2 \pi-5)^{2}$
$=8 \pi^{2}-40 \pi+50$
