Question

8*sin^2*25p/24*cos^2*23p/24-1

Answer 1

$8sin^2 (\frac{25\pi }{24})*cos^2(\frac{23\pi}{24})-1 =8*[\frac{1}{2}*sin(\frac{25\pi}{24}-\frac{23\pi}{24})+sin(\frac{25\pi}{24}+\frac{23\pi}{24})]^2\\ \\ -1=8*(\frac{1}{2}*sin\frac{\pi}{12}+sin2\pi)^2-1=8*(\frac{1}{2}*sin\frac{\pi}{12}+0)^2-1=\\ \\ =8*\frac{1}{4}*sin^2\frac{\pi}{12}-1=2*\frac{1-cos\frac{\pi}{6}}{2}-1=1-cos\frac{\pi}{6}-1=-cos\frac{\pi}{6}=-\frac{\sqrt{3}}{2}$

P.S. Формулы:

$sina*cosb= \frac{1}{2} [sin(a-b)+sin(a+b)] \\ \\ sin^2 a= \frac{1-cos(2a)}{2}$