Question:
stion Prove the following identities (1-16)
$\sec ^{4} x-\sec ^{2} x=\tan ^{4} x+\tan ^{2} x$
Solution:
$\mathrm{LHS}=\sec ^{4} x-\sec ^{2} x$
$=\sec ^{2} x\left(\sec ^{2} x-1\right)$
$=\left(\tan ^{2} x+1\right)\left(\tan ^{2} x\right) \quad\left(\because \sec ^{2} x-\tan ^{2} x=1\right)$
$=\tan ^{4} x+\tan ^{2} x$
$=$ RHS
Hence proved.