Question

Решите уравнение: (sin ⁡x + cos ⁡x)² = 1+ sin ⁡x cos ⁡x

Answer 1

(sin ⁡x + cos ⁡x)² = 1+ sin ⁡x cos ⁡x

sin x² +2sin x cos x+cos x²=1+sin x cos x

1+sin 2x =1+sin x cos x

sin 2x=sin x cos x

sin 2x-sin x cos x=0

2 sin x cos x - sin x cos x=0

sin x cos x=0

sin x=0 cos x=0

x=kπ, k∈Z x=π/2 +kπ, k∈Z

x=kπ/2, k∈Z

Answer 2

sin^2x+cos^2x+2sinxcosx=1+sinxcosx

1+2sinxcosx=1+sinxcosx

sinxcosx=0

sinx=0

x=пn , n∈Z

cosx=0

x=п/2 +пn, n∈Z

x=пn/2