Question

proove that tan50-tan40=2tan10

Answer 1

Answer:

tan50-tan40=2tan10

tan50 = 2tan10+tan40

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

tan50-tan40=2tan10

Answer 2

Step-by-step explanation:

tan50 - tan40

= sin50/cos50 - sin40/cos40

= (sin50*cos40 - cos50*sin40)/(cos40*cos50)

= sin(50-40)/(cos40*cos50)

= sin10/(cos40*cos50)

multiplying numerator and denominator by 2

2sin10/(2cos40*cos50)

=2sin10/{cos(50-40) + cos(50+40)}

= 2sin10/(cos10 + cos90)

= 2sin10/(cos10 + 0).........since cos90 = 0

= 2sin10/cos10

= 2tan10

RHS