Question

Вычислить: cos^4(pi/8)-sin^4(pi/18) Помогите пожалуйста.

Answer 1

$\cos^4 \frac{\pi}{8} -\sin^4 \frac{\pi}{8} =(\cos^2 \frac{\pi}{8} -\sin^2 \frac{\pi}{8} )\underbrace{(\cos^2 \frac{\pi}{8} +\sin^2 \frac{\pi}{8} )}_{1}=\\ \\ \\ =\cos^2 \frac{\pi}{8} -\sin^2 \frac{\pi}{8} =\cos(2\cdot \frac{\pi}{8} )=\cos \frac{\pi}{4}= \frac{1}{\sqrt{2}}$