prove tan squared theta over sin squared theta = 1 +tan squared theta

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- May 4th 2010, 04:56 PMway123identity
prove tan squared theta over sin squared theta = 1 +tan squared theta

- May 4th 2010, 05:02 PMharish21
$\displaystyle \frac{tan^{2}x}{sin^{2}x} = \frac{\frac{sin^{2}x}{cos^{2}x}}{sin^{2}x} = \frac{sin^{2}x}{cos^{2}x} \times \frac{1}{sin^{2}x} = \frac{1}{cos^2x}$

$\displaystyle = sec^{2}x$

you should know that $\displaystyle sec^{2}x-tan^{2}x = 1$

therefore, $\displaystyle sec^{2}x = 1+ tan^{2}x$