Component Identities

[brandon26]

Solve for x

3sin(x+10)=4cos(x-10)

I tried changinf everything into tan nothing out. I tried expaning the brackets and collecting like terms, that didnt work out either.
Please help.

[Astronuc]

Refer to trigonometric identities.

cos (a + b) = cos a cos b - sin a sin b

sin (a + b) = sin a cos b + cos a sin b

http://mathworld.wolfram.com/TrigonometricAdditionFormulas.html

[brandon26]

Yeh, but I cant simplify anything to solve the problem

[Astronuc]

Well expand the sin and cos and apply cos (-x) = cos x, and sin (-x) = -sin x.

Then collect terms/coefficients of cos x and sin x.

If one has a form A cos x = B sin x, the tan x = A/B and x = tan-1 (A/B). In this problem A and B have terms of sin 10 and cos 10.