A) 10
B) 11
C) 12
D) 13
Correct Answer: D
Solution :
Given expression \[=3{{[{{(\sin x-\cos x)}^{2}}]}^{2}}+\] \[6{{(\sin c+\cos x)}^{2}}+4({{\sin }^{6}}x+{{\cos }^{6}}x)\] \[=3{{[{{\sin }^{2}}x+{{\cos }^{2}}x-2\sin x\,\cos x]}^{2}}+6[{{\sin }^{2}}x+{{\cos }^{2}}x\]\[+2\sin x\,\cos x]\] \[+4[({{\sin }^{2}}x+{{\cos }^{2}}x)\,({{\sin }^{2}}x+{{\cos }^{2}}x-{{\sin }^{2}}x\,{{\cos }^{2}}x]\] \[=3{{[1-\sin 2x]}^{2}}+6[1+\sin 2x]\] \[+4\times 1\times [{{({{\sin }^{2}}x+{{\cos }^{2}}x)}^{2}}-3{{\sin }^{2}}x{{\cos }^{2}}x]\] \[=3[1+{{\sin }^{2}}2x-2\sin 2x]+6+6\sin 2x\] \[+(4-3\,{{\sin }^{2}}2x\] \[=13\]
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