Question

Выразите |sinx-cosx| через a, если sinx+cosx=a.

Answer 1

Решение прицеплено в картинке.

Answer 2

sinx+cosx=a
sinx+sin(π/2-x)=2sinπ/4cos(x-π/4)=√2cos(x-π/4)=a
cos(x-π/4)=a/√2
sin(x-π/4)=√(1-cos²(x-π/4))²=√(1-a²/2)=√(2-a²)/√2
sinx-cosx=sinx-sinx(π/2-x)=2sin(x-π/4)cosπ/4=√2sin(x-π/4)
|sinx-cosx|=|√2sin(x-π/4)|=√2*√(2-a²)/√2=√(2-a²)