Question

Prove that 2tan10+tan40=tan50

Answer 1

Answer:

proved

Step-by-step explanation:

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 is helpful

Answer 2

Äñ§WÈR

we have

tan(A-B) = (tan A - tan B)/(1+tan A tan B)

put A = 50 and B = 40

LHS = tan 10

RHS =

$(tan 50 - tan 40)/(1+ tan 40 \: tan 50)$

$= (tan 50 - tan 40)/2 \: because \: tan \: 40 \: tan 50 = tan 40 \: cot 40 =1$

$so \: 2 \: tan \: 10 = tan \: 50 - tan \: 40</p><p> \: or \: tan 50 = tan \: 40 + 2 \: tan 10</p><p> \: \: proved$

hope its help u