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
B
π2
C
0
D
π

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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