Lakhbir
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Formula of integration of cosec x in terms of tan
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username3555092
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\displaystyle \text{cosec}(x) \equiv \text{cosec} (x)\frac{\text{cosec}(x)+ \text{cot}(x)}{\text{cosec}(x)+ \text{cot}(x)

 

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Keep \displaystyle \frac{\mathrm{d}}{\mathrm{d}x} \text{ln}f(x) in mind.

Edit: a more direct approach to get it in terms of tan is using the substitution \displaystyle t=\tan{\frac{x}{2}} (a popular substitution for trig integrals).
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