>>291
(sinθ-cosθ)^2 = 1/4
1-2sinθcosθ = 1/4
cos(2θ) = 3/4

(sinθ)^2 - (cosθ)^2 = - cos(2θ) = -3/4


{1/sinθ}＋{1/cosθ} =2√2のとき

cosθ + sinθ = 2(√2) sinθcosθ
1+2sinθcosθ= 8 (sinθcosθ)^2
k = 2 sinθcosθ = cos(2θ)
2k^2 -k -1 = (2k+1)(k-1) = 0
k = -1/2

sinθcosθ = -1/4
sinθ+cosθ = (√2)k = -(√2)/2

x^3 +y^3 = (x+y)^3 - 3xy(x+y)