Question

Prove tan(θ / 2) = sin θ / (1 + cos θ) for θ in quadrant 1 .

Answer 1

We are asked to prove tan(θ / 2) = sin θ / (1 + cos θ). In this case, tan θ is equal to sin θ / cos θ. we can apply this to the equality. sin θ is equal to square root of (1-cos θ)/2 while cos θ is equal to square root of (1 + cos θ)/2.
Hence, when we replace cos θ with square root of (1-cos θ)/2, we can prove already.

Answer 2

Answer:

Step-by-step explanation:

We have to prove the identity$tan(\frac{\Theta }{2})=\frac{sin\Theta}{1+cos\Theta }$

We will take right hand side of the identity

$\frac{sin\Theta}{1+cos\Theta}=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{1+[2cos^{2}(\frac{\Theta }{2})-1]}$

$=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{2cos^{2}(\frac{\Theta }{2})}$$=\frac{sin(\frac{\Theta }{2})}{cos(\frac{\Theta }{2})}$

$=tan(\frac{\Theta }{2})$ [ Tan θ will be positive since θ lies in 1st quadrant ]

= L. H. S.

Hence proved.