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Introduction of Trigonometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry1 Mark
MCQ
$\left(\sec ^4 A-\sec ^2 A\right)=$
  • A
    $\tan^4A-\tan^2A$
  • ✓
    $\tan ^2 A+\tan ^4 A$
  • C
    $\tan ^2 A-\tan ^4 A$
  • D
    None of these
✓

Answer

Correct option: B.
$\tan ^2 A+\tan ^4 A$
We have, $\left(\sec ^4 A=\sec ^2 A\right)$
$=\sec ^2 A\left(\sec ^2 A-1\right)=\sec ^2 A\ \left(1+\tan ^2 A-1\right)$
$=\sec ^2 A \tan ^2 A=\left(1+\tan ^2 A\right) \tan ^2 A= \left(\tan ^2 A+\tan ^4 A\right)$

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