A) \[\left( \left. -\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}} \right] \right.\]
B) \[[0,1)\]
C) \[\left. \left[ \frac{1}{\sqrt{2}},1 \right. \right)\]
D) \[(-1\,,1)\]
Correct Answer: B
Solution :
\[\sin \,{{\cos }^{-1}}(\cos \,({{\tan }^{-1}}x))=p\] For \[x\in R\] \[{{\tan }^{-1}}x\in (-\pi \text{/}2,\,\,\pi \text{/}2)\] \[\therefore \] \[\cos ({{\tan }^{-1}}x)\in (0,1]\] \[\therefore \] \[{{\cos }^{-1}}cos\,({{\tan }^{-1}}x)\in [0,\pi \text{/}2)\] \[\therefore \] \[\sin \,({{\cos }^{-1}}(\cos \,({{\tan }^{-1}}x)))\in [0,\,1)\]
You need to login to perform this action.
You will be redirected in
3 sec
