Given that tan B= 7/24 with B in quadrant III, find sin 2B, cos 2B, and tan 2B, using angle identities.

Answer 1

Did you recognize the 7-24-25 right-angled triangle?
then sin B = -7/25
cos B = -24/25

sin 2B = 2sinBcosB = 2(-7/25)(-24/25) = 336/625
cos2B = cos^2B - sin^2B = 576/625- 49/625 = 527/625

tan2B = sin2B/cos2B = (336/625)÷(527/625) = 336/527