Question

If $2sinx-cos2x=1$, then $co{s}^{2}x+co{s}^{4}x$ is equal to

• A. $1$
• B. $-1$
• C. $-\sqrt{5}$
• D. $\sqrt{5}$

Answer 1

The correct option is A

$1$

Given $2sinx+2si{n}^{2}x-1=1$

Or,$si{n}^{2}x+sinx-1=0$

$\therefore sinx=\frac{-1\pm \sqrt{1+4}}{2}=\frac{-1+\sqrt{5}}{2}$

$\Rightarrow si{n}^{2}x=\frac{3-\sqrt{5}}{2}\Rightarrow co{s}^{2}x=\frac{\sqrt{5}-1}{2}$

$\therefore co{s}^{2}x(1+co{s}^{2}x)=\frac{\sqrt{5}-1}{2}\times \frac{\sqrt{5}+1}{2}=1$