Question

provethat 2tan10°+tan40°=tan50°​

Answer 1

Ello..✌✌

we know,

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

So,

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

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

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

=> tan50 - tan50 tan40 tan10 = tan40 + tan10

tan50 - tan50 tan40 tan10 = tan40 + tan10

and we know tan50 = tan (90-40) = cot40

tan50 = tan (90-40) = cot40 => tan50 - cot40 tan40 tan10 = tan40 + tan10

=> tan50 - tan10 = tan40 + tan10

Since cot40= 1/tan40

=> tan50 = tan40 + 2tan10

Hence, proved..