A) \[1+2\sin x\sin y\sin z\]
B) \[1-2\sin x\sin y\sin z\]
C) \[1+2\cos x\cos y\cos z\]
D) \[1-2\cos x\cos y\cos z\]
Correct Answer: C
Solution :
| As, \[x+y=z\] ?(i) |
| Also,\[{{\cos }^{2}}x+{{\cos }^{2}}y+{{\cos }^{2}}z\] |
| \[=1+({{\cos }^{2}}x-{{\sin }^{2}}y)+{{\cos }^{2}}z\] |
| \[=1+\cos \,\,(x+y)\cos \,\,(x-y)+{{\cos }^{2}}z\] |
| \[=1+\cos \,\,(z)\cos \,\,(x-y)+{{\cos }^{2}}z\] [from Eq. (i)] |
| \[=1+\cos \,\,z\,\,[cos\,\,(x-y)+\cos \,\,(x+y)]\] |
| \[=1+\cos z\left[ 2\cos \frac{(x-y+x+y)}{2}\cos \frac{(x+y-x+y)}{2} \right]\]\[=1+2\cos z\cos x\cos y=1+2\cos x\cos y\cos z\] |
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