A) \[12\]
B) \[13\]
C) \[14\]
D) \[11\]
Correct Answer: B
Solution :
\[3{{(\sin x-\cos x)}^{4}}+6{{(\sin x+\cos x)}^{2}}\] \[+4({{\sin }^{6}}x+{{\cos }^{6}}x)\] \[=3{{(1-2\sin x\cos x)}^{2}}+6(1+2\sin \,x\,\cos \,\,x)\]\[+4({{\sin }^{2}}x+{{\cos }^{2}}x)({{\sin }^{4}}x+{{\cos }^{4}}x-{{\sin }^{4}}x\,{{\cos }^{2}}x)\] \[=3[1+4{{\sin }^{2}}x\,{{\cos }^{2}}x-4\sin x\,\cos x]\] \[+6+12\sin x\,\cos x+4[{{({{\sin }^{2}}x+{{\cos }^{2}}x)}^{2}}\] \[-2{{\sin }^{2}}x\,{{\cos }^{2}}x-{{\sin }^{2}}x\,{{\cos }^{2}}x]\] \[=3+12{{\sin }^{2}}{{\cos }^{2}}x+6+4-12{{\sin }^{2}}x{{\cos }^{2}}x\] \[=13\]
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