A) 0
B) sin A cos B
C) cos A cos B
D) tan A tan B
Correct Answer: A
Solution :
Given expression \[=\frac{({{\sin }^{2}}A-{{\sin }^{2}}B)+(co{{s}^{2}}A-{{\cos }^{2}}B)}{(\cos A-\cos \,\,B)(sin\,\,A-sin\,\,B)}\] \[=\frac{({{\sin }^{2}}A+{{\cos }^{2}}A)-({{\sin }^{2}}B+{{\cos }^{2}}B)}{(\cos A-\cos B)(\sin A-\sin B)}\] \[=\frac{(1-1)}{(\cos A-\cos B)(\sin A-\sin B)}=0\]
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