A) \[0\]
B) \[1\]
C) \[-1\]
D) None of these
Correct Answer: C
Solution :
| [c] We have, |
| \[2({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )\] |
| \[=2({{\sin }^{6}}\theta +{{\cos }^{6}}\theta -{{\sin }^{4}}\theta -{{\cos }^{4}}\theta )-({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )\]\[=2{{\sin }^{4}}\theta ({{\sin }^{2}}\theta -1)+2{{\cos }^{4}}\theta ({{\cos }^{2}}\theta -1)-({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )\]\[=-2{{\sin }^{4}}\theta {{\cos }^{2}}\theta -2{{\cos }^{4}}\theta {{\sin }^{2}}\theta -({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )\]\[[{{\sin }^{2}}\theta -1=-{{\cos }^{2}}\theta ,{{\cos }^{2}}\theta -1=-{{\sin }^{2}}\theta ]\] |
| \[=-2{{\sin }^{2}}\theta {{\cos }^{2}}\theta ({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )-({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )\]\[=-(2{{\sin }^{2}}\theta {{\cos }^{2}}\theta +{{\sin }^{4}}\theta +{{\cos }^{4}}\theta )\] |
| \[=-{{({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )}^{2}}=-{{(1)}^{2}}=-1\] |
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