Question

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"

Answer 1

because the domain of tangent function is 0 to pi, theta/2 is needs to be in the first quadrant.

Answer 2

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

Answer 3

Sorry in thf first steo it wont be tan^2 theta/2 but just tan theta/2

Answer 4

@Somjit How did you get sqrt(1-cos(theta)/(1+cos(theta))

Answer 5

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

Answer 6

this will hold for any theta it is not necessary that it is in the first quadrant