Quite straightforward question, given a trigonometric equation $a \cdot \sin (x + k) = b \cdot \cos( x - k )$ how can one find the solution. e. g. $3 \cdot \sin(x + π/6) = 2 \cdot \cos( x - π/6 )$.
Thanks in advance.
Trigonometric equations of the form $a \cdot \sin(x + k) = b \cdot \cos(x - k)$
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trigonometry
1 Answers
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Hint. Use the sine-of-a-sum and cosine-of-a-sum formulae to expand, collect terms to get $$A\sin x+B\cos x=0$$ for some constants $A,B$. Rearranging, $$\tan x=-\frac BA\ .$$ You will have to be careful if any coefficients turn out to be zero. I'm sure you can fill in the details for yourself.