Question

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

Answer 1

$8sin^2 (frac{25pi }{24})*cos^2(frac{23pi}{24})-1 =8*[frac{1}{2}*sin(frac{25pi}{24}-frac{23pi}{24})+sin(frac{25pi}{24}+frac{23pi}{24})]^2\ \ -1=8*(frac{1}{2}*sinfrac{pi}{12}+sin2pi)^2-1=8*(frac{1}{2}*sinfrac{pi}{12}+0)^2-1=\ \ =8*frac{1}{4}*sin^2frac{pi}{12}-1=2*frac{1-cosfrac{pi}{6}}{2}-1=1-cosfrac{pi}{6}-1=-cosfrac{pi}{6}=-frac{sqrt{3}}{2}$

P.S. Формулы:

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