Question

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

Answer 1

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

Answer 2

(sin ⁡x + cos ⁡x)² = 1+ sin ⁡x cos ⁡x

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

sinxcosx=0

sinx=0; x=пk, k∈Z

cosx=0; x=п/2+пk, k∈Z