Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

$\begin{array}{rl}& \sin x+{\sin }^{2}x=1\\ & \Rightarrow \sin x={\cos }^{2}x\Rightarrow \tan x=\cos x\end{array}$
$\therefore$ Given expression
$\begin{array}{rl}& =2{\cos }^{12}x+6\left[{\cos }^{10}x+{\cos }^{8}x\right]+2{\cos }^{6}x\\ & =2\left[{\sin }^{6}x+3{\sin }^{5}x+3{\sin }^{4}x+{\sin }^{3}x\right]\\ & =2{\sin }^{3}x\left[(\sin x+1{)}^3\right]\\ & =2{\left[{\sin }^{2}x+\sin x\right]}^3\\ & =2\end{array}$