How do you simplify the expression ${tan}^{2} x {csc}^{2} x - {tan}^{2} x$ $tan^2xcsc^2x-tan^2x$ ?

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Answer 1 · 2016-10-13T02:20:46

The expression simplifies to $1$ $1$ .

$= {tan}^{2} x ({csc}^{2} x - 1)$ $=tan^2x(csc^2x - 1)$

$= \frac{{sin}^{2} x}{{cos}^{2} x} (\frac{1}{{sin}^{2} x} - 1)$ $=sin^2x/cos^2x(1/sin^2x - 1)$

$= \frac{1}{{cos}^{2} x} - \frac{{sin}^{2} x}{{cos}^{2} x}$ $= 1/cos^2x - sin^2x/cos^2x$

$= \frac{1 - {sin}^{2} x}{{cos}^{2} x}$ $=(1 - sin^2x)/cos^2x$

$= \frac{{cos}^{2} x}{{cos}^{2} x}$ $=cos^2x/cos^2x$

$= 1$ $= 1$

Hopefully this helps!

How do you simplify the expression tan^2xcsc^2x-tan^2xtan2xcsc2x−tan2xtan^2xcsc^2x-tan^2x?