How do you simplify ${sec}^{2} x {tan}^{2} x + {sec}^{2} x$ $sec^2x tan^2x + sec^2x$ ?

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Answer 1 · 2018-03-14T15:18:11

${sec}^{4} x$ $sec^4x$

${sec}^{2} x {tan}^{2} x + {sec}^{2} x$ $sec^2xtan^2x+sec^2x$

$\Rightarrow {sec}^{2} x ({tan}^{2} x + 1)$ $=> sec^2x(tan^2x+1)$

The identity for $({tan}^{2} x + 1)$ $(tan^2x+1)$ is equal to ${sec}^{2} x$ $sec^2x$

$\Rightarrow {sec}^{2} x ({sec}^{2} x)$ $=> sec^2x(sec^2x)$

$\Rightarrow {sec}^{4} x$ $=> sec^4x$

How do you simplify sec2xtan2x+sec2xsec^2x tan^2x + sec^2x?