If cosx + cos2x = 1,the numerical value of (sin12 + 3sin10x + 3sin8x + sin6x - 1) = ?
If cosx + cos2x = 1,the numerical value of (sin12 + 3sin10x + 3sin8x + sin6x - 1) = ? Correct Answer 0
$$\eqalign{ & {\sin ^{12}} + 3{\sin ^{10}}x + 3{\sin ^8}x + {\sin ^6}x - 1 \cr & \Rightarrow {\left( {{{\sin }^4}x + {{\sin }^2}x} \right)^3} - 1 \cr & \Rightarrow {\left( {{{\cos }^2}x + {{\sin }^2}x} \right)^3} - 1 \cr & \left \cr & (\cos x = 1 - {\cos ^2}x = {\sin ^2}x) \cr & \Rightarrow 1 - 1 \cr & \Rightarrow 0 \cr} $$
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Feb 20, 2025
