题目

设cos2Sita=-3分之根号2,求sin四次Sita+cos四次Sita的值

提问时间：2021-02-25

答案

cos2θ = -√2 /3
cos2θ = 1- 2sin²θ
所以 1- 2sin²θ = -√2 /3
sin²θ = (3+√2)/6
cos²θ = 1-(3+√2)/6 = (3-√2)/6
sin^4 θ +cos^4 θ = (sin²θ + cos²θ)² - 2sin²θ cos²θ
= 1² - 2 *(3+√2)/6* (3-√2)/6
= 1 - 2*(9-2)/36
= 1- 7/18
= 11/18