Question

integrate sinx-cosx/sinx+cosx​

Answer 1

Step-by-step explanation:

by using the trigonometry identities

Answer 2

Answer:

$→\int \frac{ \sin(x) - \cos(x) }{ \sin(x) + \cos(x) } dx \\ Let \: \sin(x) + \cos(x) = t \\(cos(x)-sin(x))dx=dt\\- (sin(x) - \cos(x) )dx =dt\\(sin(x)-cos(x))dx=-dt \\ → -\int \frac{dt}{t} =- log |t| +C\\ =- log |( \sin(x) + \cos(x) ) | + C$

• -log|(sin(x)+cos(x)|+C is the right answer.