Why can't \(\displaystyle{\frac{{{1}}}{{{\sin{{x}}}{\cos{{x}}}}}}\) be expressed in the

Jackson Floyd

Jackson Floyd

Answered question

2022-03-23

Why can't 1sinxcosx be expressed in the form Asinx+Bcosx
1sin(x)cos(x)=Asinx+Bcosx1=Acosx+Bsinx
I let x=π2, getting A=-1. Then I let x=π, getting B=1. This means that 1=cosxsinx which is obviously wrong most of the time.

Answer & Explanation

horieblersee275

horieblersee275

Beginner2022-03-24Added 17 answers

we can write this as
-4i(e-ix-eix)(e-ix+eix)

So by letting u=eix we can write this as
4i(1uu)(1u+u)=4iu2(1u2)(1+u2)=4i2(u2+1)4i4(u+1)+4i4(u1)
assuming I did my calculations correctly. Note that this isn't going to combine together in the way you want. Partial fractions are fundamentally property of rational functions of polynomials.

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