A) \[\sin \,\,A\sin \,\,B\sin \,\,C\]
B) \[\cos \,\,A\cos \,\,B\cos \,\,C\]
C) \[\tan \,\,A\,\,\tan \,\,B\,\,\tan \,\,C\]
D) 1
Correct Answer: B
Solution :
\[(1+\sin A)(1+\sin B)(1+\sin C)=\] \[(1-\sin A).(1-\sin B)(1-SinC)=x\](Let) \[\therefore \]\[x,\,\,x=(1+\sin A)(1+\sin B)\] \[(1+\sin C)(1-\sin A)(1-\sin B)(1-\sin C)\] \[\Rightarrow \]\[{{x}^{2}}=(1-{{\sin }^{2}}A)(1-{{\sin }^{2}}B)(1-{{\sin }^{2}}C)\] \[\Rightarrow \]\[{{x}^{2}}={{\cos }^{2}}A\cdot {{\cos }^{2}}B\cdot {{\cos }^{2}}C\] \[\Rightarrow \]\[x=\pm \cos A.\cos B.\cos C\]
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