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To prove (1-cosx)/sinx = tan(x/2)

To prove (1-cosx)/sinx = tan(x/2)

Grade:12

2 Answers

Sunil Kumar FP
askIITians Faculty 183 Points
6 years ago
1-cosx=2sin^2x/2
sinx=2sinx/2cosx/2
therefore 1-cosx/sinx=tanx/2
thanks and regards
sunil kr
askIITian faculty
Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
\frac{1-cosx}{sinx}=tan\frac{x}{2}…..............(1)
cosx = 1-2sin^{2}\frac{x}{2}
1-cosx = 2sin^{2}\frac{x}{2}
sinx = 2sin\frac{x}{2}.cos\frac{x}{2}
Put in (1)
\frac{1-cosx}{sinx} = \frac{2sin^{2}\frac{x}{2}}{2sin\frac{x}{2}.cos\frac{x}{2}} = \frac{sin\frac{x}{2}}{cos\frac{x}{2}} = tan\frac{x}{2}
Cheers!
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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