решите уравнение cos2x + sin2x = 0,25

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