Question

Найдите 16( sin^3 t + cos^3 t ), если sin t + cos t = 0,5

Answer 1

16( sin^3 t + cos^3 t ) = 16(sin t+cos t)(sin^2 t-sin t*cos t+cos^2 t) = 16*0.5*(1-sin t*cos t) =8*(1-sin t*cos t)
(sin t + cos t)^2 = 0,25
sin^2 t + 2cos t*sin t + cos^2 t = 0.25
cos t*sin t = (0.25-1)/2=-0,375
8*(1-sin t*cos t)=8*(1-(-0,375)) = 11