A) \[co{{s}^{2}}\text{ }A\]
B) \[co{{s}^{2}}\text{ }A-1\]
C) \[si{{n}^{2}}\text{ }A\]
D) \[1\]
Correct Answer: C
Solution :
\[{{\cos }^{2}}\,B+{{\cos }^{2}}(A-B)\] \[-2\cos \,A\,\cos B\,\cos \,(A-B)\] \[={{\cos }^{2}}\,B+\cos \,(A-B)\,[\cos \,A\,\cos \,B\] \[-2\,\cos \,A\,\cos \,B]\] \[={{\cos }^{2}}\,B+\cos \,(A-B)\,[\cos \,A\,\,\cos \,B\] \[+\sin \,A\,\,\sin B-2\,\cos \,A\,\cos \,B]\] \[={{\cos }^{2}}\,B-\cos \,(A-B)\,\cos \,(A+B)\] \[={{\cos }^{2}}B\,-[{{\cos }^{2}}B-\,{{\sin }^{2}}A]\] \[={{\sin }^{2}}A\]
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