Solve h(x)=g(x) without Calculator: General Solution

[DERRAN]

Homework Statement

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

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

Homework Equations

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

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

 

[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.

 

[DERRAN]

Thank you very much Дьявол