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

Mathematics · Inverse Trigonometric Functions

JEE Main 2024 — 31 January, Shift 2 — Question 16

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

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

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

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

Answer key and solution verified before publishing.

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