Question

$3(\sin x-\cos x{)}^4+6(\sin x+\cos x{)}^2+4({\sin }^{6}x+{\cos }^{6}x)$ equal to-

• A. $11$
• B. $12$
• C. $13$
• D. $14$

Answer 1

Answer: (C)

$13$

$\Rightarrow 3({\sin }^{2}x+{\cos }^{2}x-\sin 2x{)}^2+6({\sin }^{2}x+{\cos }^{2}x+\sin 2x)+4({\sin }^{2}x+{\cos }^{2}x\left)\right({\sin }^{4}x+{\cos }^{4}x-{\sin }^{2}x{\cos }^{2}x)$

$\Rightarrow 3(1-\sin 2x{)}^2+6(1+\sin 2x)+4(1-3{\sin }^{2}x{\cos }^{2}x)$

$\Rightarrow 3(1-\sin 2x{)}^2+6(1+\sin 2x)+4(1-3{\sin }^{2}x{\cos }^{2}x)$

$\Rightarrow 3+3{\sin }^{2}2x-6\sin 2x+6+6\sin 2x+4-3{\sin }^{2}2x=13$