Use the addition or subtraction formula for cosine to compute $\cos(-5\pi/12)$ (Leave your answer in exact form.)
I have $$\begin{align}\cos(-5\pi/12)&=\cos((\pi/4)-(5\pi/6))\\
&=\cos(\pi/4)\cos(5\pi/6)+\sin(\pi/4)\sin(5\pi/6)\\
&=\frac{\sqrt2}2\cdot\frac{\sqrt3}2+\frac{\sqrt2}2\cdot\frac 12\end{align}$$
Is this right?
Best Answer
Alternative, you can use the half-angle formula (I am aware that this was not specified):
$$\cos{\left(-\frac{5 \pi}{12}\right)} = \sqrt{\frac{1+\cos{(-5 \pi/6)}}{2}} = \frac{\sqrt{2-\sqrt{3}}}{2}$$
Now, $2-\sqrt{3} = (\sqrt{3}-1)^2/2$
so that
$$\cos{\left(-\frac{5 \pi}{12}\right)} = \frac{\sqrt{3}-1}{2 \sqrt{2}} = \frac{\sqrt{6}-\sqrt{2}}{4}$$