Question

How do you solve `sin(2x)+2cosx=0` and find all solutions in the interval `0<=x<360`?

Answer 1

The solutions are `x ={90,270}`

Explanation:

To solve this equation, we use
`sin2x= 2sinxcosx`

`sin2x+2cosx=0`

`2sinxcosx+2cosx=2cosx(sinx+1)=0`

`cosx=0` and `sinx+1=0` `=>` `sinx=-1`

As `x in [0, 360[`

`x=90` or `270` and `x=270`