prove that tan 50 = 2 ta n 10 + ta n 40
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