if sin x+cos x=a then |sinx-cosx|

Question

whose solve this problum as early as possible

Answer 1

sin(x) + cos(x) = a

 

[sin(x) + cos(x)][sin(x) - cos(x)] = sin²x - cos²x

 

Use trigonometric identity:  cos(2x) = cos²x - sin²x

 

sin²x - cos²x = -cos(2x)

 

Therefore,

 

[sin(x) + cos(x)][sin(x) - cos(x)] = -cos(2x)

 

a [sin(x) - cos(x)] = -cos(2x)

 

sin(x) - cos(x) = -(1/a) cos(2x)

 

|sin(x) - cos(x)| = |(1/a) cos(2x)|