Math, asked by pp4837337, 9 months ago

proove this plz URGENT!!! i will mark u brainliest...

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Answered by hr855213

SRY I tried but can't able to find

Answered by silentloffer

$you \: know$

$(x - y)(x + y) = {x}^{2} - {y}^{2}$

$\huge\purple {Question:}$

$(sec \theta + cos\theta)(sec \theta - cos \theta) = ({sec}^{2} \theta - {cos}^{2} \theta)$

${sec}^{2} \theta(1 - \frac{ {cos}^{2} \theta }{ {sec}^{2} \theta } )$

${sec}^{2} \theta(1 - {cos}^{4} \theta) = >$

$= > {sec}^{2} \theta( {1}^{2} - ({ {cos}^{2} \theta})^{2} )$

$= > {sec}^{2} (1 + {cos}^{2} \theta)(1 - {cos}^{2} \theta)$

$= > {sec}^{2} \theta(1 + {cos}^{2} \theta)( {sin}^{2} \theta)$

$= > sin {}^{2} \theta. {sec}^{2} \theta(1 + {cos}^{2} \theta)$

$= > \frac{ {sin}^{2} \theta }{ {cos}^{2} \theta } (1 + {cos}^{2} \theta)$

$= > {tan}^{2} \theta(1 + {cos}^{2} \theta)$

$= > {tan}^{2} \theta + {tan}^{2} \theta. {cos}^{2} \theta$

$= > ( {tan}^{2} \theta + \frac{ {sin}^{2} \theta. {cos}^{2} \theta }{cos {}^{2} \theta} )$

$( {tan}^{2} \theta + {sin}^{2} \theta) \: proved...$

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