NIELIT 2023 Feb Scientist D | Section D | Question: 96

Question

If $\sin x+\sin ^{2} x=1$ then $\cos ^{8} x+2 \cos ^{6} x+\cos ^{4} x$ equals to :

• A. $0$
• B. $-1$
• C. $1$
• D. $2$

   

Answer 1

$\sin x+\sin^2x=1….(i)\implies \sin x=1-\sin^2x\implies\sin x=\cos^2x….(ii)$

$\cos^8x+2\cos^6x+\cos^4x$ can be written as:

$\implies(\cos^4x)^2+(\cos^2x)^2+2*(\cos^4x)^2(\cos^2x)^2$

$\left [ \because a^2+b^2+2ab=(a+b)^2) \right ]$

$\implies (\cos^2x+\cos^4x)^2$

$\implies (\sin x+\sin^2x)^2$ (from eq (ii))

$\implies1^2=1$