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Introduction of Trigonometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry1 Mark
MCQ
$\left(\cos ^4 x-\sin ^4 x\right)$ is equal to
  • A
    $2 \sin ^2 x-1$
  • B
    $1-2 \cos ^2 x$
  • C
    $\sin ^2 x-\cos ^2 x$
  • ✓
    $2 \cos ^2 x-1$
✓

Answer

Correct option: D.
$2 \cos ^2 x-1$
$: \cos ^4 x-\sin ^4 x$
$=\left(\cos ^2 x+\sin ^2 x\right)\left(\cos ^2 x=\sin ^2 x\right)$
$=1\left(\cos ^2 x-\left(1-\cos ^2 x\right)\right\}$
$=\cos ^2 x-1+\cos ^2 x$
$=2 \cos ^2 x-1$

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