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Mathematics · 2023 · 2 marks
Inverse Trigonometric FunctionsBasic Concepts of Inverse Trigonometric Functions2 marksApplyvery short answer
CBSE 2023 · Region 2 · Set 1 · Q21
(a) Evaluate sin^-1( sin (3 π)/4)+ cos^-1( cos π)+ tan^-1(1)
(a)
Evaluate $\displaystyle \sin ^{-1}\left(\sin \frac{3 \pi}{4}\right)+\cos ^{-1}(\cos \pi)+\tan ^{-1}(1)$
OR
(b)
Draw the graph of $\displaystyle \cos ^{-1} x$, where $\displaystyle x \in[-1,0]$. Also, write its range. $\displaystyle 2$
Marking-scheme solution
$$\begin{aligned}
& \sin ^{-1}\left(\sin \frac{3 \pi}{4}\right)+\cos ^{-1}(\cos \pi)+\tan ^{-1}(1)=\frac{\pi}{4}+\pi+\frac{\pi}{4} \\
& =\frac{3 \pi}{2}
\end{aligned}
$$
Or
Correct Graph
Range: $\displaystyle \left[\frac{\pi}{2}, \pi\right]$
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