A) 3
B) 1
C) 2
D) - 1
Correct Answer: B
Solution :
We have,\[{{\cos }^{-1}}p+{{\cos }^{-1}}q+{{\cos }^{-1}}r=\pi \]we know that, if \[y={{\cos }^{-1}}x\], then\[-1\le x\le 1\] and \[0\le y\le \pi \], Hence the given equation will hold only when each is k \[\therefore \] \[p=q=r=\cos \pi =-1\] \[\therefore \] \[{{p}^{2}}+{{q}^{2}}+{{r}^{2}}+2pqr\] \[={{(-1)}^{2}}+{{(-1)}^{2}}+{{(-1)}^{2}}+2(-1)\,\,(-1)\,(-1)\] \[=1+1+1-2=3-2=1\]You need to login to perform this action.
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