Question

use one or more of the six sum and difference identities to find the

sin(75°)

find the exact value of the expression.

sin(75°)=□
(simplify your answer. type an exact answer, using radicals

Explanation:

Step1: Express \(75^{\circ}\) as a sum of two known angles

We know that \(75^{\circ}=45^{\circ} + 30^{\circ}\).

Step2: Use the sine sum identity

The sine sum identity is \(\sin(A + B)=\sin A\cos B+\cos A\sin B\).
Here \(A = 45^{\circ}\) and \(B=30^{\circ}\).
We know that \(\sin45^{\circ}=\frac{\sqrt{2}}{2}\), \(\cos45^{\circ}=\frac{\sqrt{2}}{2}\), \(\sin30^{\circ}=\frac{1}{2}\), \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\).
Substitute these values into the identity:

$$
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$$

Answer:

\(\frac{\sqrt{6}+\sqrt{2}}{4}\)