Precalc. help!

Question

Using angle sum and difference formula please help me solve these 2 problems. If sin(theta)= 12/13 with o<theta< pi/2. Find exact value of tan (theta/2) . Also my second question is if csc theta=7/6 and costheta>0. Find exact value of sin(2theta).

Answer 1

Draw and label a diagram.

 

sin θ = 12/13 ⇒ cos θ = 5/13

 

tan θ/2 = ±√[(1 - cos θ) / 1 + cos θ)]

 

Substitute values and calculate