Question

Sin2x+sinx in factored form

Answer 1

Recall that sin(2x) = 2sinxcosx
Proof of sin(2x):

`sin(2x) = sin(x + x)`

Using the Addition property:

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


`\therefore sin(2x) + sin(x) = 2sin(x)cos(x) + sin(x)`

`= sin(x)[2cos(x) + 1]`