Lorraine Harvey

2021-12-31

The Question

$\int \mathrm{csc}(x-\frac{\pi}{3})\mathrm{csc}(x-\frac{\pi}{6})dx$

What I Tried- I tried dividing both numerator and denominator by$\mathrm{sin}\frac{\pi}{6}$ but couldnt

What I Tried- I tried dividing both numerator and denominator by

boronganfh

Beginner2022-01-01Added 33 answers

Hint

$\mathrm{csc}(x-\frac{\pi}{3})\mathrm{csc}(x-\frac{\pi}{6})$

$=\frac{1}{\mathrm{sin}(\frac{\pi}{3}-\frac{\pi}{6})}\cdot \frac{\mathrm{sin}(x-\frac{\pi}{6}-(x-\frac{\pi}{3}))}{\mathrm{sin}(x-\frac{\pi}{3})\mathrm{sin}(x-\frac{\pi}{6})}$

hysgubwyri3

Beginner2022-01-02Added 43 answers

Now, let

The denominator has two simple real roots. Then partial fraction decomposition to face two simple integrals.

Vasquez

Expert2022-01-08Added 669 answers

Substitute

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