A) 2
B) 0
C) 4
D) 6
Correct Answer: B
Solution :
We have \[2({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1\] \[=2[{{({{\sin }^{2}}\theta )}^{3}}+{{({{\cos }^{2}}\theta )}^{3}}]-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1\] \[=2[({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )({{\sin }^{4}}\theta +{{\cos }^{4}}\theta -{{\sin }^{2}}\theta \]\[{{\cos }^{2}}\theta )]-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1\] \[=[2{{\sin }^{4}}\theta +2{{\cos }^{4}}\theta -2{{\sin }^{2}}\theta {{\cos }^{2}}\theta ]-3{{\sin }^{4}}\theta -3{{\cos }^{4}}\theta +1\] \[=-{{({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )}^{2}}+1=-{{1}^{2}}+1=-1+1=0\]You need to login to perform this action.
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