Trigonometric Integration Watch

shomkin
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#1
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Integrate (tanx)/(1 + cosx) dx.

Ive tried this so many times but can't get the answer! Help
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Speleo
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Multiply by (1-cosx)/(1-cosx), then rearrange a little.
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shomkin
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(Original post by Speleo)
Multiply by (1-cosx)/(1-cosx), then rearrange a little.
I just did that and I get: cosecx(secx - 1). I can't seem to simplify it let alone integrate it.
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gyrase
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(Original post by shomkin)
Integrate (tanx)/(1 + cosx) dx.

Ive tried this so many times but can't get the answer! Help
tanx/(1 + cosx)
= 1/sinxcosx - cosecx
= 1/(sin(2x)/2) - cosecx
= 2/sin(2x) - cosecx
= 2cosec(2x) - cosecx

standard integral
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