Question

n: Prove that tan 70° - tan 20° = 2 tan 50°​

Answer 1

i) tan(20) = tan(70 - 50) = {tan(70) - tan(50)}/{1 + tan(70)*tan(20)}

ii) Cross multiplying, tan(20) + tan(20)*tan(70)*tan(50) = tan(70) - tan(50)

==> tan(20) + tan(50) = tan(70) - tan(50)

[since tan(20) = cot(90 - 20) = cot(70); so tan(20)*tan(70) = cot(70)*tan(70) = 1]

Rearranging the above, tan(20) + 2*tan(50) = tan(70)