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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
$\sqrt{2+\sqrt{2+2 \cos 4 \theta}}=$
  • A
    $\cos \theta$
  • B
    $\sin \theta$
  • ✓
    $2 \cos \theta$
  • D
    $2 \sin \theta$
✓

Answer

Correct option: C.
$2 \cos \theta$
(C)
$2+2 \cos 4 \theta=2(1+\cos 4 \theta)$
$=4 \cos ^2 2 \theta$ …(i)
$\therefore \sqrt{2+\sqrt{2+2 \cos 4 \theta}}=\sqrt{2+2 \cos 2 \theta} \ldots[$ From (i) $]$
$=\sqrt{2(1+\cos 2 \theta)}$
$=\sqrt{4 \cos ^2 \theta}=2 \cos \theta$

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