Question

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

Answer 1

`x=0,\pi,2\pi`

Step-by-step 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`)