Question

Prove that Tan50°-Tan40°=2Tan10°

Answer 1

we have tan(a+b) = (tan a +tan b)/(1-tan a tan b)

tan(40+10) = (tan40+ tan10)/(1-tan40tan10)

tan50 = (tan40+ tan10)/(1-tan40tan10)

tan50(1-tan40tan10)=tan40+ tan10

tan50-tan50tan40tan10 = tan40+tan10

and tan50 = tan(90-40) = cot40

=> tan50-cot40tan40tan10 = tan40+ tan10

tan50-tan10 = tan40+ tan10

because cot40= 1/tan40

tan50 = tan40+2tan10