Question

How do you solve `sin^2 x + 2 sin x cos x = 0`?

Answer 1

Hence solution is `x=npi` or `x=npi+arctan(-2)`

Explanation:

As `sin^2x+2sinxcosx=0`

`sinx(sinx+2cosx)=0`

i.e. either `sinx=0` i.e. `x=npi`

or `sinx+2cosx=0` i.e. `sinx=-2cosx` or `tanx=-2`

Hence `x=arctan(-2)` or `x=npi+arctan(-2)`

Hence, `x=npi` or `x=npi+arctan(-2)`