SOLUTION: Prove the following identity (2tanx-sin2x)/(2sin^2×)=tanx

Question 1179268: Prove the following identity

(2tanx-sin2x)/(2sin^2×)=tanx

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Unless you have a huge amount of experience with solving trig identities, change everything to sines and cosines. And of course use the double angle formula to replace sin(2x).

You won't learn much from this if I finish the problem for you....

Here is what you need to do from here:
(1) combine the expressions in the numerator using the least common denominator, cos(x);
(2) rewrite the expression (a fraction within a fraction) as a single fraction;
(3) factor the numerator;
(4) use the identity to rewrite the fraction;
(5) simplify the fraction;
(6) verify that what you have left is equal to tan(x)

RELATED QUESTIONS
2tanx-sin2x/2sin^2x = tanx Prove the identity (answered by greenestamps)

prove the identity: a) cot((x+pi)/(2)) = -tanx b) tanx = (1 - cos2x)/... (answered by MathLover1)

Prove the following is an identity: 1) (1 - cos2x)/( sin2x) = tanx (answered by Alan3354)

PLEASE help prove the identity? (1-cos2x)/tanx = sin2x (answered by MathLover1)

Prove the following identity: {{{(1-sin2x)/(cos2x) =... (answered by Alan3354)

Prove : tanx +... (answered by MathLover1)

Prove the identity: A) Sinx( sec x-csc x) = tanx-1 B) (cot x-1)^2 = 1-sin2x/ sin^2 x (answered by lwsshak3)

Prove the identity: Sin2x (tan x + cot x) = 2... (answered by lwsshak3)

Prove this identity {{{ (sin2x + cos2x -1) / (sin2x + cos2x +1) }}} = {{{ (1 - tanx )/... (answered by drj)