Корень из 3 cos (x+45) + sin (x+45) = корень из 2

(√ 3) cos (x+45°) + sin (x+45°) = √ 2

a cos (x) + b sin (x) = c ⇔a / (√a²+b²) cos (x) + b / (√a²+b²) sin (x) = c / (√a²+b²)

[ (√ 3) / (2) ]·cos (x+45°) + (1/2) ·sin (x+45°) = (√ 2) / 2

cos φ=[ (√ 3) / (2) ]

sinφ=[1/2] tgφ=1/√3

cosφ ·cos (x+45) + sinφ ·sin (x+45°) = (√ 2) / 2

cos ((x+π/4) - φ) = (√ 2) / 2

1) ((x+π/4) - φ) = π/4+2πn, n∈Z ⇒ x1=φ+2πn,

2) ((x+π/4) - φ) = - π/4+2πn, n∈Z ⇒x2 = - π/2+φ+2πn