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FP2 Integration

Using t = tan(x/2), integrate 1/1-sinx
I have differentiated t and got dt/dx = 1/2 sec^2(x/2) and then rearranged to get dx = 2dt/sec^2(x/2). So I know dx = 2dt/(1+t^2) but I'm not sure what to do with the sinx.

Reply 1

DFranklin

A standard result you should know if doing the "t = tan x/2" substitution is that sin x = 2t/(1+t^2).

Reply 2

Toast210

Original post by DFranklin

A standard result you should know if doing the "t = tan x/2" substitution is that sin x = 2t/(1+t^2).

Ah really? Tbf, this is OCR and I'm doing OCR MEI but I have never come across this before. I didn't think it was that different between exam boards.

Reply 3

DFranklin

Original post by Toast210

Ah really? Tbf, this is OCR and I'm doing OCR MEI but I have never come across this before. I didn't think it was that different between exam boards.

I don't know what's officially in any exam board, but if you are using that substitution you should work out how and remember how to express sin x, cos x and tan x in terms of t.

Reply 4

Toast210

Original post by DFranklin

I don't know what's officially in any exam board, but if you are using that substitution you should work out how and remember how to express sin x, cos x and tan x in terms of t.

Thanks I appreciate it. Do you know where I could find the proofs for these expressions? I find it easier to remember them if I know how they are derived.

Reply 5

Interea

Original post by Toast210

Thanks I appreciate it. Do you know where I could find the proofs for these expressions? I find it easier to remember them if I know how they are derived.