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8. Introduction to Trigonometry
easy
Show that $\tan ^{4} \theta+\tan ^{2} \theta=\sec ^{4} \theta-\sec ^{2} \theta$
Option A
Option B
Option C
Option D
Solution
L.H.S. $=\tan ^{4} \theta+\tan ^{2} \theta=\tan ^{2} \theta\left(\tan ^{2} \theta+1\right)$
$=\tan ^{2} \theta \cdot \sec ^{2} \theta$ $\left[\because \sec ^{2} \theta=\tan ^{2} \theta+1\right]$
$=\left(\sec ^{2} \theta-1\right) \cdot \sec ^{2} \theta$ $\left[\because \tan ^{2} \theta=\sec ^{2} \theta-1\right]$
$=\sec ^{4} \theta-\sec ^{2} \theta=$ R.H.S.
Standard 10
Mathematics
