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Recently, I came across a beautiful question. I tried several ways of solving it, but I could not reach anywhere. The question goes like:

Prove that:

$$a\sin x+b\cos x=\sqrt{a^2+b^2} \sin\left(x+\tan^{-1}\left(\frac{b}{a}\right)\right)$$

Please give me a hint. Thanks in advance.

ibuprofen
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    Divide and multiply LHS by $\sqrt(a^2+b^2)$ , and recall the formulae for sine and cos . (opposite/hyp , etc. ) . Then see if you can use any sum formula... – Sinπ Apr 22 '19 at 18:23
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    Consider $C\sin(x+\theta)=a\sin x+b\cos x$, then expand the LHS using trig addition formulae, then compare coefficients. Are you sure you searched this correctly, it's very well known. The first link on Google – John Doe Apr 22 '19 at 18:24
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    I marked this as a duplicate of a particular question (since I happen to remember that I posted an answer to it), but there are other instances on Math.SE. See, for instance, here and here. I'm sure you can find at least a few more. Searching is a little tricky, but looking through the "Related" questions can be helpful. – Blue Apr 22 '19 at 18:30

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