Question

if 2 cos squared theta + 3 cos theta is equals to 2 then find cos theta

Answer 1

Let cos be x

2x2+3x-2=0

(2x-1)(x+2)=0

(2cosx-1)(cosx+2)=0

2cosx-1=0

2cosx=1

Cosx=1/2

Cosx=60

Answer 2

Answer:

$\cos\theta=\frac{1}{2}$          

Step-by-step explanation:

Given : Expression $2\cos^2\theta+3\cos\theta=2$

To find : The value of $\cos\theta$?

Solution :

Expression $2\cos^2\theta+3\cos\theta=2$

Let $\cos\theta=x$

Then,  $2x^2+3x-2=0$

Solving the quadratic equation by middle term split,

$2x^2+4x-x-2=0$

$2x(x+2)-1(x+2)=0$

$(2x-1)(x+2)=0$

$(2x-1)=0,(x+2)=0$

$x=\frac{1}{2},x=-2$

Substitute back,

$\cos\theta=\frac{1}{2}$

$\cos\theta=-2$ but it is not possible as cos x value lie between -1 and 1.

Therefore, $\cos\theta=\frac{1}{2}$