Question

Given tan⁡θ=3/4 and sin⁡〖θ)]<0, find tan⁡2θ.


a. 1/3 b. √5/3 c. 5/9 d. 24/7 e. None of these

Answer 1

If tan(θ)>0 and sin(θ)<0, then cos(θ)<0, and so:
tan(2θ) = (2tan⁡(θ))/(1-〖tan〗^2 (θ)) = (2×(3/4))/(1-〖(3/4)〗^2 ) = 24/7