Question

19 simplify the expression $\cos^{2}(28^{\circ})-\sin^{2}(28^{\circ})$ by using a double - angle formula.

Explanation:

Step1: Recall the double - angle formula

The double - angle formula for cosine is \(\cos(2\alpha)=\cos^{2}\alpha-\sin^{2}\alpha\).

Step2: Substitute \(\alpha = 28^{\circ}\)

Let \(\alpha = 28^{\circ}\), then \(\cos^{2}(28^{\circ})-\sin^{2}(28^{\circ})=\cos(2\times28^{\circ})\).

Step3: Calculate the value

\(2\times28^{\circ}=56^{\circ}\), so \(\cos(2\times28^{\circ})=\cos(56^{\circ})\).

Answer:

\(\cos(56^{\circ})\)