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Trigonometric Identities — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTrigonometric Identities1 Mark
MCQ
$\tan ^4 \theta+\tan ^2 \theta=$
  • A
    $\sec ^2 \theta-2 \sec ^4 \theta$
  • B
    $2 \sec ^2 \theta-2 \sec ^4 \theta$
  • C
    $\sec ^2 \theta-\sec ^4 \theta$
  • ✓
    $\sec ^4 \theta-\sec ^2 \theta$
✓

Answer

Correct option: D.
$\sec ^4 \theta-\sec ^2 \theta$
(D) $\sec ^4 \theta-\sec ^2 \theta \tan ^4 \theta+\tan ^2 \theta$
$=\tan ^2 \theta\left(\tan ^2 \theta+1\right)$
$=\tan ^2 \theta \sec ^2 \theta=\left(\sec ^2 \theta-1\right) \sec ^2 \theta$
$=\sec ^4 \theta-\sec ^2 \theta$.

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