If cosx + cos2x = 1,the numerical value of (sin12 + 3sin10x + 3sin8x + sin6x - 1) = ?
A. -1
B. 2
C. 0
D. 1
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\sin ^{12}} + 3{\sin ^{10}}x + 3{\sin ^8}x + {\sin ^6}x - 1 \cr & \Rightarrow {\left( {{{\sin }^4}x + {{\sin }^2}x} \right)^3} - 1 \cr & \Rightarrow {\left( {{{\cos }^2}x + {{\sin }^2}x} \right)^3} - 1 \cr & \left[ {\cos x + {{\cos }^2}x = 1} \right] \cr & (\cos x = 1 - {\cos ^2}x = {\sin ^2}x) \cr & \Rightarrow 1 - 1 \cr & \Rightarrow 0 \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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