Question

Find the solution
2cos2x-2cosx=0

Answer 1

Answer:

x = 0, 2π/3, 4π/3

Step-by-step explanation:

2 cos(2x) − 2 cos x = 0

Use double angle formula.

2 (2 cos²x − 1) − 2 cos x = 0

Simplify.

4 cos²x − 2 − 2 cos x = 0

2 cos²x − 1 − cos x = 0

2 cos²x − cos x − 1 = 0

Factor.

(cos x − 1) (2 cos x + 1) = 0

Solve.

cos x = 1 or -½

x = 0, 2π/3, 4π/3

Answer 2

To solve this problem, we have to use trigonometric function in which we can use some trigonometric equations on this. The solutions to this equation is

$\pi , \frac{\pi}{3}, \frac{5\pi}{3}$

Trigonometric Functions

We would apply a simple mathematical rule here;

$a(b+c)=ab+ac$

Let's substitute our functions and solve

$2cos(2x)+2cosx=0\\2(2cos^2x-1)+2cosx=0\\4cos^2x-2+2cosx=0\\2cos^2x+cosx-1=0\\2cos^2x=2cosx-cosx-1=0\\2cos^2x+cosx-1=0$

We can solve the quadratic equation and get a solution to this problem.

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

Using factorization method,

$cosx+1 = 0\\cosx = -1\\x = cos^-^1(-1)\\x = \pi$

The second solution is

$2cosx-1=0\\2cosx=1\\cosx=\frac{1}{2} \\x = cos^-^1(\frac{1}{2} \\x = \frac{\pi}{3}, \frac{5\pi}{3}$

From the above calculations, the solutions to this equation is

$\pi , \frac{\pi}{3}, \frac{5\pi}{3}$

Learn more on trigonometric functions here;

https://brainly.com/question/2437614

#SPJ2