cos2x + sin2x =0,25
cos²х - sin²х + 2 sinх·cosх = 0.25
делим на cos²х
1 - tg²x + 2tgx = 0.25
0.75 - tg²x + 2tgx = 0
или
tg²x - 2tgx - 0.75 = 0
D = 4 + 3 = 7
√D = √7
tgx₁ = (2 - √7):2 = 1 - 0.5 √7 = - (0.5√7 - 1)
tgx₂ = (2 +√7):2 = 1 + 0.5 √7 = 0.5√7 + 1
x₁ = -arctg(0.5√7 - 1) + πn
x₂ = arctg(0.5√7 + 1) + πn