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How do I prove this trig identity?

I have to prove:
sinx/(1+cosx) + (1-cosx)/sinx = 2tan(x/2)

I'm up to 2sinx/1+cosx, but I don't know how to go from there.
Any help would be appreciated! Thanks! :smile:
Reply 1
Avatar for TeeEm
TeeEm
19
Original post by кяя
I have to prove:
sinx/(1+cosx) + (1-cosx)/sinx = 2tan(x/2)

I'm up to 2sinx/1+cosx, but I don't know how to go from there.
Any help would be appreciated! Thanks! :smile:




sinA = 2sinA/2cosA/2

since

sin2A = 2sinAcosA


similarly the cosine
Reply 2
Avatar for Zacken
Zacken
22
Original post by кяя

I'm up to 2sinx/1+cosx, but I don't know how to go from there


You might want to write sin⁡x=2sin⁡x2cos⁡x2\sin x = 2 \sin \frac{x}{2} \cos \frac{x}{2} and cos⁡x=2cos⁡2x2−1\cos x = 2 \cos^2 \frac{x}{2} - 1
Reply 3
Avatar for кяя
кяя
OP
11
Original post by TeeEm
sinA = 2sinA/2cosA/2

since

sin2A = 2sinAcosA


similarly the cosine


Original post by Zacken
You might want to write sin⁡x=2sin⁡x2cos⁡x2\sin x = 2 \sin \frac{x}{2} \cos \frac{x}{2} and cos⁡x=2cos⁡2x2−1\cos x = 2 \cos^2 \frac{x}{2} - 1


Thank you both of you so much!!
Reply 4
Avatar for TeeEm
TeeEm
19
Original post by кяя
Thank you both of you so much!!


my pleasure
Reply 5
Avatar for Zacken
Zacken
22
Original post by кяя
Thank you both of you so much!!


You're very welcome! :-)

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