Question

sint*cost= -12
тогда чему равно sin^4t+cos^4t ???

Answer 1

Sint * Cost = - 1/2

(SintCost)² = (- 1/2)²

Sin²tCos²t = 1/4

2 * Sin²t * Cos²t = 1/4 * 2

2Sin²tCos²t = 1/2

Sin⁴t + Cos⁴t = (Sin²t + Cos²t)² - 2Sin²tCos²t = 1 - 1/2 = 1/2

Answer 2

sin^4(t) +cos^4(t) =sin^4(t)+2sin^2(t)cos^2(t)+cos^4(t) - 2sin^2(t)cos^2(t)=(sin^2(t)+cos^2(t)) ^2 - 2(sin(t)cos(t))^2 =

=1-2(-1/2)^2=1-1/2=1/2=0,5