prove thattan40+2tan10=tan50?

Answer 1

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

Answer 2

When you're proving an identity you can't treat it like an equation where you can "move" things to the other side. You start with one side and work with it until you've gotten the other side. So, a basic identity is

tan 50 = tan (10 + 40)
= ( tan 10 + tan 40) / ( 1 - tan 10 tan 40)

and another is tan 40 tan 50 = tan 40 cot 40 = 1.

So tan 40 + 2 tan 10 =
tan 40 + tan 10 + tan 10 =
tan 50(1 - tan 40 tan 10) + tan 10 =
tan 50 - tan 50 tan 40 tan 10 + tan 10 =
tan 50 - 1 • tan 10 + tan 10 =
tan 50

Answer 3

tan50=tan10 +tan40/1-tan10tan40
taking denominator to other side
tan50-tan50tan10tan40=tan10+tan40

now
tan40=cot50=1/tan50
hence puting tan40tan50=1in orignal equation

tan50=tan40+2tan10

Answer 4

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
or tan 50 = tan 40 + 2 tan 10
proved

Hats of them who says you cannot tranfser from LHS to RHS. wrong back ground

Answer 5

Here is a simple way to prove it.

Want: tan(40) + 2tan(10) = tan(50)......(1)

Proof.
tan(10)
= tan(50-40)
= [tan(50)-tan(40)]/[1+tan(50)tan(40)]......
= [tan(50)-tan(40)]/[1+cot(40)tan(40)]......
= (1/2) [tan(50)-tan(40)]......(2)

Plug in (2) to the left side of (1),
tan(40) + 2tan(10)
= tan(40) + tan(50) - tan(40)
= tan(50)

Answer 6

tan40+2tan10=tan40+tan10+tan10=tan60 and not tan50

Answer 7

hi friend ,
tarundeep has proved it right ... so check it and know the solution ...