Plz solve 3rd part
Q.3. Total number of ordered pairs (x, y) satisfying | y | = cos x and y = $\sin { }^{-1}\left(\sin x\right) where \left|x\right|\le 3\mathrm{\pi }$ is equal to:
(A) 2
(B) 4
(C) 6
(D) 8

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{We} \mathrm{have} \\ \left|\mathrm{y}\right|=\mathrm{cosx}....\left(\mathrm{i}\right) \\ \mathrm{y}={\sin }^{-1}\left(\mathrm{sinx}\right)....\left(\mathrm{ii}\right) \\ \mathrm{By} \left(\mathrm{i}\right) \mathrm{and} \left(\mathrm{ii}\right) \\ \left|{\sin }^{-1}\left(\mathrm{sinx}\right)\right|=\mathrm{cosx} \\ \mathrm{Now} \\ \left|\mathrm{x}\right|\le 3\mathrm{\pi } \\ \mathrm{Hence} \\ -3\mathrm{\pi }\le \mathrm{x}\le 3\mathrm{\pi } \\ \mathrm{Now} \mathrm{we} \mathrm{will} \mathrm{draw} \mathrm{graph} \mathrm{of} \mathrm{both} \left|{\sin }^{-1}\left(\mathrm{sinx}\right)\right| \mathrm{and} \mathrm{cosx} \mathrm{in} -3\mathrm{\pi }\le \mathrm{x}\le 3\mathrm{\pi } \\ \mathrm{and} \mathrm{count} \mathrm{number} \mathrm{of} \mathrm{point} \mathrm{of} \mathrm{intersection} \mathrm{to} \mathrm{get} \mathrm{number} \mathrm{of} \mathrm{solutions}. \end{gathered}$$


As there are 6 points of intersection, hence there will be 6 solutions.

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