Question

tan50 equal to 2tan40+tan10

Answer 1

tan50= tan(40+10) 

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


hope it help