Question

1. find the exact value of the expression sin 15°

Explanation:

Step1: Use the sine subtraction formula

$\sin(A - B)=\sin A\cos B-\cos A\sin B$. Let $A = 45^{\circ}$ and $B = 30^{\circ}$. Then $\sin15^{\circ}=\sin(45^{\circ}-30^{\circ})$.

Step2: Substitute the values of trigonometric functions

We know that $\sin45^{\circ}=\frac{\sqrt{2}}{2}$, $\cos45^{\circ}=\frac{\sqrt{2}}{2}$, $\sin30^{\circ}=\frac{1}{2}$, $\cos30^{\circ}=\frac{\sqrt{3}}{2}$.
Substituting into the formula:

$$
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Answer:

$\frac{\sqrt{6}-\sqrt{2}}{4}$