A) \[\frac{\pi }{2}\]
B) \[-\pi \]
C) \[\pi \]
D) \[-\frac{\pi }{2}\]
Correct Answer: D
Solution :
[d] \[{{\sin }^{-1}}[\cos \{{{\cos }^{-1}}(\cos \,x)+{{\sin }^{-1}}(\sin \,x)\}]\] \[={{\sin }^{-1}}[\cos (x+\pi -x)]\] as \[x\in (\pi /2,\pi )\] \[={{\sin }^{-1}}(cos\pi )=si{{n}^{-1}}(-1)=-\frac{\pi }{2}\]
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