If cosx + cos2x = 1,the numerical value of (sin12 + 3sin10x + 3sin8x + sin6x - 1) = ?

Answer: Option C

$$\begin{array}{rl}& {\sin }^{12}+3{\sin }^{10}x+3{\sin }^{8}x+{\sin }^{6}x-1\\ & \Rightarrow {\left({\sin }^{4}x+{\sin }^{2}x\right)}^3-1\\ & \Rightarrow {\left({\cos }^{2}x+{\sin }^{2}x\right)}^3-1\\ & \left[\cos x+{\cos }^{2}x=1\right]\\ & (\cos x=1-{\cos }^{2}x={\sin }^{2}x)\\ & \Rightarrow 1-1\\ & \Rightarrow 0\end{array}$$