<s>[INST] General solution of $(\sqrt3 - 1)\sin\theta + (\sqrt3 + 1)\cos\theta =2 $ Find general solution of the equation $(\sqrt3 - 1)\sin\theta + (\sqrt3 + 1)\cos\theta =2 $.
My approach:
Squared on both sides, formed a quadratic equation in $\cos\theta$ and finally got two solutions for theta,
$$\theta = 2n\pi \pm \frac{\pi}{6}$$
$$\theta = 2n\pi \pm \frac{\pi}{3}$$
But the answer given in my book is $$2n\pi \pm \frac{\pi}{4} + \frac{\pi}{12}$$
Pretty strange
can anyone help me?
 [/INST] In general, to solve $a \cos x +b\sin x=c$. Divide both sides by $\sqrt{a^2+b^2}$ and then let $\sin \alpha =\frac{a}{\sqrt{a^2+b^2}}$ to get
$$\sin (x+\alpha)=\frac{c}{\sqrt{a^2+b^2}}$$
Now solve for $x$.
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