If $\sin x+\sin ^{2} x=1$, then $\cos ^{8} x+2 \cos ^{6} x+\cos ^{4} x$ is

If $\sin x+\sin ^{2} x=1$, then $\cos ^{8} x+2 \cos ^{6} x+\cos ^{4} x$ is
  1. 3
  2. 2
  3. 1
  4. 4

Solution

Given $\sin x+\sin ^{2} x=1 \Rightarrow \sin x=1-\sin ^{2} x$ $\begin{aligned} \therefore \sin x=\cos ^{2} x \Rightarrow \sin ^{2} x &=\cos ^{4} x \\ \cos ^{8} x+2 \cos ^{6} x+\cos ^{4} x &=\left(\cos ^{4} x+\cos ^{2} x\right)^{2} \\ &=\left(\sin ^{2} x+\cos ^{2} x\right)^{2}=1 \end{aligned}$

Asked in: MHT CET 2020 (15 Oct Shift 2)

Practice more Trigonometric Equations questions on Aicharya