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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
$2 \sin A \cos ^3 A-2 \sin ^3 A \cos A =$
  • A
    $\sin 4 A$
  • ✓
    $\frac{1}{2} \sin 4 A$
  • C
    $\frac{1}{4} \sin 4 A$
  • D
    $\frac{1}{8} \sin 4 A$
✓

Answer

Correct option: B.
$\frac{1}{2} \sin 4 A$
(B)
$2 \sin A \cos ^3 A-2 \sin ^3 A \cos A$
$=2 \sin A \cos A \left(\cos ^2 A-\sin ^2 A\right)$
$=2 \sin A \cos A \cos 2 A$
$-\sin 2 A \cos 2 A$
$=\frac{1}{2} \sin 4 A$

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