This is kind of a new type of question for me:
If $\alpha$ and $\beta$ are two different roots of the equation $a\cos\theta + b\sin\theta = c$, then show that
$$\sin(\alpha+\beta) = \frac{2ab}{a^2 + b^2}$$
Could someone please explain the procedure to me?
write the equation in the form $$\frac{a}{\sqrt{a^2+b^2}}\cos(\theta)+\frac{b}{\sqrt{a^2+b^2}}\sin(\theta)=\frac{c}{\sqrt{a^2+b^2}}$$ and define $$\sin(\gamma)=\frac{b}{\sqrt{a^2+b^2}}$$ and $$\cos(\gamma)=\frac{a}{\sqrt{a^2+b^2}}$$ and you will get $$\cos(\gamma)\cos(\theta)+\sin(\gamma)\sin(\theta)=\frac{c}{\sqrt{a^2+b^2}}$$ so $$\cos(\gamma-\theta)=\frac{c}{\sqrt{a^2+b^2}}$$