Question

integration of Cos⁴x-sin⁴x/cosx-sinx dx​

Answer 1

Step-by-step explanation:

We have,

$\int \frac{ \cos^{4} (x) - \sin ^{4} ( x ) }{ \cos(x) - \sin(x) } dx$

$= \int \frac{( \cos^{2} (x) - \sin ^{2} (x) )( \cos^{2} (x) + \sin ^{2} (x) ) }{ \cos(x) - \sin(x) } dx$

$= \int \frac{( \cos(x) - \sin(x))( \cos(x) + \sin(x) ) }{ \cos(x) - \sin(x) } dx$

$= \int \cos(x)dx + \int\sin(x) dx$

$= - \sin(x) + \cos(x) + c$