Question

What are the solutions for cos2 x - cos2x = 0​

Answer 1

Answer:

$x=0,\pi,2\pi$

Explanation:

$cos^{2}(x)-cos(2x)=0$

Firstly, we will simplify the double angle formulae

$cos(2x)=cos(x+x)\\cos(x+x)=cos(x)cos(x)-sin(x)sin(x)\\cos(x+x)=cos^{2}(x)-sin^{2}(x)$

Now, we can substitute our value for cos(2x) into our original equation.

$cos^{2}(x)-(cos^{2}(x)-sin^{2}(x))=0\\cos^2(x)-cos^2(x)+sin^2(x)=0\\sin^2(x)=0\\sin(x)=0\\x=arcsin(0)\\x=0,\pi,2\pi$

(Solutions in the range $0 \leq x \leq 2\pi$)