Question

Решите уравнение sinx-cosx=1

Answer 1

2sinx/2*cosx/2-cos²x/2+sin²x/2-sin²x/2-cos²x/2=0
2sinx/2*cosx/2-2cos²x/2=0
2cosx/2*(sinx/2-cosx/2)=0
cosx/2=0⇒x/2=π/2+πk⇒x=π+2πk,k∈z
sinx/2-cosx/2=0/cosx/2⇒tgx/2-1=0⇒tgx/2=1⇒x/2=π/4+πk⇒x=π/2+2πk,k∈z