[Math] Trigonometry question: Find in simplest surd form: $\cos 195^{\circ}$

Question

Find in simplest surd form: $\cos 195^{\circ}$.

Ive recently been doing the trigonometry topic form textbook and have oftenly come across these questions. Can someone please justify how you do this question? Ive tried many times but no luck.

Answer 1

Assume that we are working with angles in degrees.

Hint:

$$\cos(195) = \cos(180 + 15)$$

Another hint:

Now split $\cos(180 + 15)$ using $\cos(A+B) = \cos(A)\cos(B)-\sin(A)\sin(B)$.

And another:

Substitute $\sin(180) = 0$ and $\cos(180) = -1$.

Nearly done:

Notice that $\cos(15) = \cos(30/2)$ and remember that $\cos(2A) = 2\cos^{2}(A) - 1$.

Now draw the 30/60/90 triangle and evaluate.