Question

If $\sin x+{\sin }^{2}x=1$, then the value of expression ${\cos }^{12}x+3{\cos }^{10}x+3{\cos }^{8}x+{\cos }^{6}x-1$ is equal to

• A. 1
• B. -1
• C. 2

Answer 1

Since $sinx+si{n}^{2}x=1,\Rightarrow sinx=1-si{n}^{2}x=co{s}^{2}x.....\left(i\right)$
The given expression is
$=co{s}^{6}x(co{s}^{6}x+3co{s}^{4}x+3co{s}^{2}x+1)-1=co{s}^{6}x(co{s}^{2}x+1{)}^3-1,(\because sinx=co{s}^{2}x)=(si{n}^{2}x+sinx{)}^3-1=1-1=0$