Prove that ${sec}^{2} x (1 - {cos}^{2} x) = {tan}^{2} x$ $sec^2x(1-cos^2x)=tan^2x$ ?

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Answer 1 · 2016-11-24T13:23:49

Please see below.

${sec}^{2} x (1 - {cos}^{2} x)$ $sec^2x(1-cos^2x)$

= ${sec}^{2} x - {sec}^{2} x \times {cos}^{2} x$ $sec^2x-sec^2x xx cos^2x$

= ${sec}^{2} x - \frac{1}{{cos}^{2} x} \times {cos}^{2} x$ $sec^2x-1/cos^2x xx cos^2x$

= $1+tan^2x-1/cancel(cos^2x) xx cancel(cos^2x)$

= $1+tan^2x-1$

= $tan^2x$

Prove that sec^2x(1-cos^2x)=tan^2xsec2x(1−cos2x)=tan2xsec^2x(1-cos^2x)=tan^2x?