anonymous
  • anonymous
Prove tan(θ / 2) = sin θ / (1 + cos θ) for θ in quadrant 1 I don't get the part where is says "for θ in quadrant 1"
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
because the domain of tangent function is 0 to pi, theta/2 is needs to be in the first quadrant.
anonymous
  • anonymous
if you take \[\tan ^{2} \theta/2=\sqrt(1-\cos \theta)/(1+\cos \theta)\] now you multiply both numerator and denominator by 1+cos theta, you will need to take square root of sin^2 theta, for first quadrant it is positive
anonymous
  • anonymous
Sorry in thf first steo it wont be tan^2 theta/2 but just tan theta/2

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anonymous
  • anonymous
@Somjit How did you get sqrt(1-cos(theta)/(1+cos(theta))
anonymous
  • anonymous
that is a formula you can prove it by taking tan as sin/cos and then multiply the numerator and denominator by cos theta/2 and then apply sub multiple angle formulas
anonymous
  • anonymous
this will hold for any theta it is not necessary that it is in the first quadrant
Mertsj
  • Mertsj
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Mertsj
  • Mertsj
How would you know whether to choose the positive or the negative root if you did not know which quadrant the angle is in?
anonymous
  • anonymous
Is that the answer?
anonymous
  • anonymous
think about this way. you know theta is in the first quadrant, so theta/2 is definitely in the first quadrant also. so you can just take the "positive" part in the work shown. simplify you should get the identity you're looking for.

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