Question

If A = 30°, then cos⁴ A − sin⁴ A is equal to ______.

Options

• sin 60°

• tan 60°

• cot 60°

• cos 60°

Answer 1

If A = 30°, then cos⁴ A − sin⁴ A is equal to cos 60°.

Explanation:

Substituting A = 30°:

\[\cos^4 30^\circ - \sin^4 30^\circ = \left(\frac{\sqrt{3}}{2}\right)^4 - \left(\frac{1}{2}\right)^4 = \frac{9}{16} - \frac{1}{16} = \frac{8}{16} = \frac{1}{2}\]