How do you simplify $tan^2 x- cot^2x$ ?

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Answer 1 · 2015-11-06T14:46:22

$tan^2x-cot^2x=(sin^2x)/(cos^2x)-(cos^2x)/(sin^2x)$

$=(sin^4x-cos^4x)/(sin^2x*cos^2x)$

$=((sin^2x+cos^2x)(sin^2x-cos^2x))/((1-cos^2x)(1-sin^2x)$

$=((1)(sinx+cosx)(sinx-cosx))/((1+cosx)(1-cosx)(1+sinx)(1-sinx)$

Does not appear to be able to simplify any further.

Answer 2 · 2017-03-26T19:04:41

$tan^2x-cot^2x = -4csc(2x)cot(2x)$

$tan^2x-cot^2x$

$= sin^2(x)/cos^2(x) - cos^2(x)/sin^2(x)$

$= (sin^4(x)-cos^4(x))/(cos^2(x)sin^2(x))$

$= ((sin^2x+cos^2x)(sin^2x-cos^2x)) / (cos(x)sin(x))^2$

$= ((1)(-cos(2x)))/(1/4sin^2(2x))$

$=-4cos(2x)/sin^2(2x)$

$= -4csc(2x)cot(2x)$

Final Answer

Answer 3 · 2017-03-27T03:27:11

$(sec^2 x - csc^2 x)$

Add 1 and (- 1) into the equation:
$f(x) = (tan^2 x + 1) - (cot^2 x + 1) =$
$f(x) = sec^2 x - csc^2 x$

How do you simplify tan^2 x- cot^2xtan^2 x- cot^2x?