A) -3
B) 0
C) 1
D) 3
Correct Answer: C
Solution :
\[6({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-9({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+4\] \[=6[{{({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )}^{3}}-3{{\sin }^{2}}\theta {{\cos }^{2}}\theta ({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )]\]\[-9[{{({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )}^{2}}-2{{\sin }^{2}}\theta {{\cos }^{2}}]+4\] \[=6[1-3{{\sin }^{2}}\theta {{\cos }^{2}}\theta ]-9\,[1-2{{\sin }^{2}}\theta {{\cos }^{2}}\theta ]+4\] \[=6-9+4=1\].You need to login to perform this action.
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