How do you simplify $\frac{{tan}^{2} (x)}{1 + {tan}^{2} (x)}$ $(tan^2(x))/(1+tan^2(x))$ ?

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How do you simplify $\frac{{tan}^{2} (x)}{1 + {tan}^{2} (x)}$ $(tan^2(x))/(1+tan^2(x))$ ?

1 Answer

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Answer 1 · 2016-08-01T04:34:39

${sin}^{2} x$ $sin^2 x$

Explanation:

Simplify $f (x) = \frac{{tan}^{2} x}{1 + {tan}^{2} x}$ $f(x) = tan^2 x/(1 + tan^2 x)$
Use trig identity:
$1 + {tan}^{2} x = \frac{1}{{cos}^{2} x}$ $1 + tan^2 x = 1/(cos^2 x)$
$f (x) = \frac{{sin}^{2} x}{{cos}^{2} x} (\frac{{cos}^{2} x}{1}) = {sin}^{2} x$ $f(x) = (sin^2 x)/(cos^2 x)(cos^2 x/1) = sin^2 x$

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How do you simplify $\frac{{tan}^{2} (x)}{1 + {tan}^{2} (x)}$ $(tan^2(x))/(1+tan^2(x))$ ?

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Explanation:

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How do you simplify $\frac{{tan}^{2} (x)}{1 + {tan}^{2} (x)}$ $(tan^2(x))/(1+tan^2(x))$ ?