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I was watching this video on orthogonal signals and the author used a trigonometric equality that I haven't seen before (at the bottom of the screenshot):

Could anyone tell me where I can find a proof of this?

qed
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1 Answers1

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As in the image, $\sin\left(\theta+\dfrac\pi2\right)=\cos\theta$

Now $A\sin(wt+\psi)+B\sin(wt+\phi)=\sin wt(A\cos\psi+B\cos\phi)+\cos wt(A\sin\psi+B\sin\phi)$

Now can you derive $p\sin x+q\cos x =\sqrt{p^2+q^2}\sin\left(x+\arcsin\dfrac p{\sqrt{p^2+q^2}}\right)$

lab bhattacharjee
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  • How do you derive the last step? – qed Jan 01 '17 at 13:06
  • @qed, See http://math.stackexchange.com/questions/948329/how-is-a-sin-theta-b-cos-theta-c-sin-theta-phi-derived OR http://www.math-only-math.com/a-cos-theta-plus-b-sin-theta-equals-c.html – lab bhattacharjee Jan 01 '17 at 13:14