SOLUTION: (Tan(x)-sin(x).cos(x)) / sin^2 (x) = tan(x)''.

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Question 889637: (Tan(x)-sin(x).cos(x)) / sin^2 (x) = tan(x)''.

Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(Tan(x)-sin(x)*cos(x)) / sin^2 (x) = tan(x)
(sin(x)/cos - sin(x)*cos(x)) / sin^2 (x) = tan(x)
(1/cos - cos(x)) / sin(x) = tan(x)
((1 - cos^2)/cos) / sin(x) = tan(x)
(sin^2/cos)/sin = tan
sin/cos = tan
tan = tan

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!

see the comments below the picture.

$$$

step 1 shows the equation.
step 2 translates tan(x) into sin(x) / cos(x).
step 3 puts everything in the numerator under the common denominator of cos(x).
step 4 factors out sin(x) from the numerator.
step 5 translates sin(x)/cos(x) back into tan(x) and translates 1 - cos^2(x) into sin^2(x).
step 6 cancels out the sin^2(x) in the numerator and the denominator and leaves you with the solution of tan(x) = tan(x) proving the identity is true.