MCQ
$\sec ^4 \theta-\sec ^2 \theta=$ ?
- A$1$
- B$\tan ^2 \theta+\sec ^2 \theta$
- ✓$\tan ^2 \theta+\tan ^4 \theta$
- D$0$
✓
Answer
Correct option: C.
$\tan ^2 \theta+\tan ^4 \theta$
$\sec ^4 \theta-\sec ^2 \theta .$
$=\sec ^2 \theta\left(\sec ^2 \theta-1\right)$
$=\quad\left(1+\tan ^2 \theta\right)\left(1+\tan ^2 \theta-1\right)$
$\quad\left[\because \sec ^2 \theta=1+\tan ^2 \theta\right]$
$=\left(1+\tan ^2 \theta\right) \tan ^2 \theta$
$=\tan ^2 \theta+\tan ^4 \theta .$
$=\sec ^2 \theta\left(\sec ^2 \theta-1\right)$
$=\quad\left(1+\tan ^2 \theta\right)\left(1+\tan ^2 \theta-1\right)$
$\quad\left[\because \sec ^2 \theta=1+\tan ^2 \theta\right]$
$=\left(1+\tan ^2 \theta\right) \tan ^2 \theta$
$=\tan ^2 \theta+\tan ^4 \theta .$
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