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Question

If $$\quad x\in \left( \cfrac { 3\pi  }{ 2 } ,2\pi  \right) $$, then the value of the expression $$\sin ^{ -1 }{ \left[ \cos { \left\{ \cos ^{ -1 }{ \left( \cos { x }  \right)  } +\sin ^{ -1 }{ \left( \sin { x }  \right)  }  \right\}  }  \right]  } $$


A
π2
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B
π2
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C
0
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D
π
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Solution

The correct option is B $$\cfrac { \pi }{ 2 } $$
$$\text{sin}^{-1}[\cos\{\text{cos}^{-1}(\cos x)+\text{sin}^{-1}(\sin x)\}]\implies \text{sin}^{-1}[\cos\{2\pi-x+x-2\pi\}]=\text{sin}^{-1}[1]=\frac{\pi}{2}$$

Mathematics

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