Question

PLEASE HELP!!!!
How to Prove:
Sin A - 2Sin^3 A/2Cos^3 A - Cos A = Tan A

Answer 1

Wait what did you mean?
(Sin A - 2Sin^3 A) / (2Cos^3 A - Cos A)
or
Sin A - (2Sin^3 A/2Cos^3 A) - Cos A?
Please use parenthesis..

Answer 2

i guess the first one is correct, dont know it is equal to TanA or not

Answer 3

Let me see:
(Sin A - 2Sin^3 A) / (2Cos^3 A - Cos A)=
Sin A [1 - 2Sin^2 A] / Cos A [ 2Cos^2 A - 1]

Answer 4

Yeah it is (Sin A - 2Sin^3 A) / (2Cos^3 A - Cos A)
= Tan A

Answer 5

Tan A = Sin A / Cos A, so now we have to prove that the rest is equal to one. So:
[1 - 2Sin^2 A] / [ 2Cos^2 A - 1]

Answer 6

working this out on paper..

Answer 7

[1 - 2Sin^2 A] / [ 2Cos^2 A - 1] =
[1 - 2 ( 1 - Cos^2 A )] / [ 2Cos^2 A - 1]

Answer 8

[1 - 2 ( 1 - Cos^2 A )] / [ 2Cos^2 A - 1] =
[1 - 2 + 2Cos^2 A )] / [ 2Cos^2 A - 1] =
[-1 + 2Cos^2 A )] / [ 2Cos^2 A - 1] =

Answer 9

[ 2Cos^2 A - 1] / [ 2Cos^2 A - 1] = 1
So there you go, it turns out to be Tan A * 1

Answer 10

Do I get good answer? haha