Question

prove that :tan50=tan40+2tan10

Answer 1

tan50 = tan(40+10) we have tan(a+b) = (tan a + tan b) / (1-tan a tan b) tan(40+10) = (tan 40 + tan10) / (1-tan 40 tan 10) tan50 = (tan40 + tan 10) / (1- tan40 tan 10) tan50 (1-tan40 tan 10) = tan40 + tan10 tan50 - tan50 tan40 tan10 = tan40 + tan10 and tan50 = tan(90-40) = cot40 => tan50 - cot40 tan40 tan10 = tan40 + tan10 tan50 - tan10 = tan40 + tan10 because cot40 = 1/tan40 tan50 = tan40 + 2tan10