Question

if 5cos(2x) + 2cos^2 (x/2) + 1 =0 find x

Answer 1

I hope it's helps you

Answer 2

Answer:

x=2nπ±π/3

Step-by-step explanation:

Since, $5cos(2x)+2cos^{2}\frac{x}{2}+1=0$

Using, $cos(2x)= 2cos^{2}x-1$

$5(2cos^{2}x-1)+2cos^{2}\frac{x}{2}+1=0$

$10cos^{2}x-5+1+cosx+1=0$$10cos^{2}x+cosx-3=0$

$10cos^{2}x+6cosx-5cosx-3=0$

$2cosx(5cosx+3)-1(5cosx+3)=0$

$(2cosx-1)(5cosx+3)=0$

If $2cosx-1=0$⇒$cosx=\frac{1}{2}$⇒$x=cos^{-1} (\frac{1}{2})$

⇒$x=\frac{\pi }{3}$

And, if $5cosx+3=0$⇒$cosx=\frac{-3}{5}$⇒$x=cos^{-1}(\frac{-3}{5})$

Therefore, In general, $x=2n\pi$±$\frac{\pi }{3}$