Question

prove that question ​

Answer 1

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Answer 2

Step-by-step explanation:

Given,

Prove that    $\sec ^{4}\Theta -\sec ^{2}\Theta =\tan ^{4}\Theta +\tan ^{2}\Theta$

We solve $LHS$

$\sec ^{2}\Theta \left ( \sec ^{2}\Theta -1 \right )$

We use identity    

$(\sec ^{2}\Theta =1+\tan ^{2}\Theta)$

$=\left ( 1+\tan ^{2}\Theta \right )\left ( 1+\tan ^{2}\Theta -1 \right )$

$=\left ( 1+\tan ^{2}\Theta \right )\tan ^{2 }\Theta$

$=\tan ^{2}\Theta +\tan ^{4}\Theta$

$=\tan ^{4}\Theta +\tan ^{2}\Theta$

We found  $LHS=RHS$