Trigonometry

15. Without using a calculator, solve 2tanθ = 1/cos30° for θ, where 0°<θ<90°.

2tanθ = 1/[√(3)/2] = 2/√3
tanθ = 1/√3
θ = 30°

16. Without using a calculator, solve √3-2tan60°sinθ = 0 for θ, where 0°<θ<90°.

√3 - 2tan60°sinθ = 0
√3 - 2√3sinθ = 0
1 - 2sinθ = 0
sinθ = 1/2
θ = 30°

17. Without using a calculator, solve (1/2)tanθ = 2(1-sin30°)sin30° for θ, where 0°<θ<90°.

(1/2)tanθ = 2(1-sin30°)sin30°
tanθ = 4(1-1/2)(1/2)
tanθ = 4(1/2)(1/2)
tanθ = 1
θ = 45°