If $a=\sin ^{-1}(\sin (5))$ and $b=\cos ^{-1}(\cos (5))$, then $a^2+b^2$ is equal to
Solution
<p>$$\begin{aligned}
& a=\sin ^{-1}(\sin 5)=5-2 \pi \\
& \text { and } b=\cos ^{-1}(\cos 5)=2 \pi-5 \\
& \therefore a^2+b^2=(5-2 \pi)^2+(2 \pi-5)^2 \\
& =8 \pi^2-40 \pi+50
\end{aligned}$$</p>
About this question
Subject: Mathematics · Chapter: Inverse Trigonometric Functions · Topic: Domain and Range
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