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# tan^2(x/2)=(secx+cosx-2)/(secx-cosx) Watch

1. I'm having a devil of a time trying to prove this with half-angle identities. Any help would be appreciated.

tan^2(x/2)=(secx+cosx-2)/(secx-cosx)

2. (Original post by falchion-gpx)
I'm having a devil of a time trying to prove this with half-angle identities. Any help would be appreciated.

tan^2(x/2)=(secx+cosx-2)/(secx-cosx)

Multiply, simplify, change to x/2
3. use for both sides the identities for 1/2 angles:

so,

substitute and simplify the RHS (and LHS) with these, and you should get =t^2 = tan^{2}(x/2)
4. Thank you for the identities. I'll put these in my list to memorize.
5. (Original post by falchion-gpx)
Thank you for the identities. I'll put these in my list to memorize.
Or put sec x as 1/cos x, tidy it up to get (1-cos x)/(1+cos x) then use the usual double angle formulae.

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