A) 0
B) -1
C) 1
D) None of these
Correct Answer: C
Solution :
\[{{\sin }^{6}}\theta +{{\cos }^{6}}\theta +3\,{{\sin }^{2}}\theta \,{{\cos }^{2}}\theta \] \[={{({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )}^{3}}-3{{\sin }^{2}}\theta {{\cos }^{2}}\theta +3{{\sin }^{2}}\theta {{\cos }^{2}}\theta =1.\] Trick: Put \[\theta ={{0}^{o}},\] we get the value of expression equal to 1. Again put \[\theta ={{45}^{o}},\] the value remains 1, it means that the expression is independent of q and is equal to 1.
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