Question

Stuck, help please !

Answer 1

Use the fundamental trigonometric equation

`\sin^2(x) + \cos^2(x) = 1 \implies \sin^2(x) = 1-\cos^2(x)`

To rewrite the equation as

`1-\cos^2(x) = 1-\cos(x)`

Subtract 1 from both sides:

`-\cos^2(x) = -\cos(x)`

Add
`\cos^2(x)` to both sides:

`\cos^2(x) - \cos(x) = 0 \iff \cos(x)\left(\cos(x)-1\right)=0`

A multipication is zero if and only if one of the factors is zero. So, the solutions are given by

`\cos(x)=0 \iff x=(\pi)/(2)+k\pi,\quad k \in \mathbb{Z}`

or

`\cos(x)-1=0 \iff \cos(x)=1 \iff x=2k\pi,\quad k \in \mathbb{Z}`