# Homework Help: General solution

1. Jun 15, 2009

### DERRAN

1. The problem statement, all variables and given/known data

h(x)=cos(x+30) and g(x) = -2sinx

Determine the general solution without the use of a calculator, if
h(x)=g(x)

2. Relevant equations

trig identities, trig ratios, double angle formulae, reduction formulae.

3. The attempt at a solution

cos(x+30)=-2sinx
sin(90-x-30)=-2sinx
sin(60-x)=-2sinx

can't get rid of the 2 in front of sinx. Need help

2. Jun 15, 2009

### Дьявол

Use the Angle sum and difference identities.

In this case:

$$\cos(\alpha \pm \beta) = \cos \alpha \cos \beta \mp \sin \alpha \sin \beta\,$$

Just substitute for alpha=x and beta=30, and you'll come up with the solution of cos(x+30).

Regards.

3. Jun 15, 2009

### DERRAN

Thank you very much Дьявол