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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
If $\cos A=\frac{3}{4}$, then the value of $2 \sin \frac{A}{2} \sin \frac{5 A}{2}=$
  • A
    $\frac{\sqrt{11}}{16}$
  • B
    $-\frac{\sqrt{11}}{16}$
  • ✓
    $\frac{11}{16}$
  • D
    $-\frac{11}{16}$
✓

Answer

Correct option: C.
$\frac{11}{16}$
(C)
$2 \sin \frac{5 A}{2} \sin \frac{A}{2}=\cos 2 A-\cos 3 A$
$=2 \cos ^2 A-1-4 \cos ^3 A+3 \cos A$
$=2\left(\frac{9}{16}\right)-1-4\left(\frac{27}{64}\right)+3\left(\frac{3}{4}\right)$$\ldots\left[\because \cos A =\frac{3}{4}\right]$
$=\frac{9}{8}-1-\frac{27}{16}+\frac{9}{4}=\frac{11}{16}$

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