proof left as an exercise

[Albert Chan]

Proof: 2*cos(30°) / (1 + 4*sin(70°)) = tan(20°)

2*cos(30°) / (1 + 4*cos(20°)) ?=? tan(20°)             // sin(70°) = cos(20°)
2*cos(30°) ?=? tan(20°) + 4*sin(20°)                     // cross multiply
cos(20°)*cos(30°) ?=? sin(20°)/2 + sin(40°)            // multiply by cos(20°)/2
sin(40°) ?=? cos(20°)*cos(30°) - sin(20°)*sin(30°)

cos(50°) = cos(20°+30°)                                       // trig angle sum identity

Proof is complete, (read it bottom-up)