Find.... tan 2A

Question

Let sin A = -15/17 with A in QIII and find the following.

tan 2A

Answer 1

tan2A = sin2A/cos2A = 2sinAcosA/(1 - 2sin²A). cosA = - √1 - sin²A = - √1 - (-15/17)² = - (1 - 225/289)^1/2 =

- 8/17.Then tan2A = 2(- 15/17)(- 8/17)/(1 - 2(- 15/17)²) = (240/289)/(1 - 450/289) = - 240/161.

Answer: tan2A = - 240/161