Question

sec^4 theeta - tan^4 theeta = 1 + 2tan^2 theeta​

Answer 1

$\bigstar\:\:\underline{\sf AnsWer :} \bigstar$

$\sf \: sec^4 \theta - tan^4 \theta = 1 + 2tan^2 \theta$

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$\bf = L. H. S$

$\sf \: = sec^{4} - tan^{4}$

$\sf \: = ( {sec}^{2} \theta + {tan}^{2} \theta)( {sec}^{2} \theta - {tan}^{2} \theta)$

$\sf \: = (1 + {tan}^{2} \theta + {tan}^{2} \theta)$

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

$\bf \: = R. H. S$

ㅤㅤ

$\bf \: L. H. S= R. H. S$

Answer 2

Answer is in Attachment. . .