A) \[{{\sin }^{2}}\theta +{{\sin }^{2}}\beta \]
B) \[{{\sin }^{2}}\theta +{{\cos }^{2}}\beta \]
C) \[{{\cos }^{2}}\theta +{{\cos }^{2}}\beta \]
D) \[{{\cos }^{2}}\theta +{{\sin }^{2}}\beta \]
Correct Answer: B
Solution :
Obviously \[x=\sin \,(\theta +\beta )\] and \[y=\sin \,(\theta -\beta )\] \[\therefore \,\,1+xy=1+\sin \,(\theta +\beta )\sin \,(\theta -\beta )\] \[=1+{{\sin }^{2}}\theta -{{\sin }^{2}}\beta ={{\sin }^{2}}\theta +{{\cos }^{2}}\beta \].
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