How Do You Correctly Expand Trigonometric Equations Involving Sine and ArcTan?

[ultrabionic_ang]

hello.. I've been having some trouble with expanding this:

(B^2+C^2)^(1/2) X sin (omega*t +(taninverse B/C)

(read as: square root of (b squared plus c squared) times sin times the quantity omega times t plus taninverse of B divided by C)

apparently, the answer is supposed to be B cos omega*t + C sin omega*t .. but I've gotten like B arctan omega^2(t) + C cos omega*t... i just wanted to know like the way to get the answer.. i think I'm using trig identities incorrectly..

 

[Tide]

What you need is \sin (x + y) = \sin x \cos y + \cos x \sin y and use the fact that \sin \tan^{-1} x = x/ \sqrt {1 + x^2} and similarly for the cosine.

 

[ultrabionic_ang]

thanks! that helped a lot! thank you!