cos6x + cos8x + 2sin3x * sin5x, если sinx = (√3)/3

Ответ:

-14/27

Объяснение:

cos6x + cos8x + 2sin3x * sin5x=cos8x+cos6x+2*1/2*(cos(5x-3x)-cos(3x+5x))= cos6x + cos8x + cos2x - cos8x =cos6x+cos2x= cos2(3x)+1-2sin²x=1- 2sin²3x+ 1-2sin²x = 2-2(3sinx-4sin³x)²-2sin²x = 2-2(3*√3/3-4*(√3/3)³)²-2*(√3/3)²=2-2(√3-4√3/9)²-2*1/3=4/3-2(5√3/9)²=4/3-50/27=-14/27