Evaluate \int \frac{dx}{\sin x-\cos x} I know it can be done by

Jazmin Perry

Jazmin Perry

Answered question

2022-01-25

Evaluate
dxsinxcosx
I know it can be done by Weierstrass substitution. But I am looking for new/simple approach. For example I tried:
1sinxcosxsinx+cosxsinx+cosxdx=sinx+cosxcos2xdx
but I can't continue from here.

Answer & Explanation

Flickkorbma

Flickkorbma

Beginner2022-01-26Added 17 answers

Write
sinxcosx=
=2(12sinx12cosx)=
=2sin(xπ4)
Larissa Hogan

Larissa Hogan

Beginner2022-01-27Added 10 answers

Hint
Using an angle sum formula gives
sinxcosx=2sin(xπ4)

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