Question

Tan70°= tan 20° + 2 tan 50°

Answer 1

tan70°-tan20°= sin70°/cos 70°-sin20°/cos20°=(sin70°cos20°-cos70°sin20°)/cos70 °cos20°

=sin50°/cos70 cos20

=2sin50/(2cos70 cos20)

=2 sin50°/(cos 90+cos50°)

=2sin 50°/cos50°

=2 tan50° since cos90=0