Question

How do you solve `8sinxcosx + 4 = 0`?

Answer 1

Using the formula for `sin(2x)`.

Explanation:

There is a trigonometric formula that tells you that

`sin(2x)=2sin(x)cos(x)`

so we can use it in the problem dividing everything by 4.

`(8sin(x)cos(x))/4+4/4=0`
`2sin(x)cos(x)+1=0`
`sin(2x)=-1`.

We know that the `sin` is equal to `-1` when the angle is `3/2pi+2npi` where n can be any integer number. So we have

`2x=3/2pi+2npi`
`x=3/4pi+npi`