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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
$1+\cos 10^{\circ}+\cos 20^{\circ}+\cos 30^{\circ}=$
  • ✓
    $4 \cos 5^{\circ} \cos 10^{\circ} \cos 15^{\circ}$
  • B
    $4 \cos 10^{\circ} \cos 20^{\circ} \cos 30^{\circ}$
  • C
    $4 \sin 5^{\circ} \sin 10^{\circ} \sin 15^{\circ}$
  • D
    $4 \sin 10^{\circ} \sin 20^{\circ} \sin 30^{\circ}$
✓

Answer

Correct option: A.
$4 \cos 5^{\circ} \cos 10^{\circ} \cos 15^{\circ}$
(A)
$1+\cos 10^{\circ}+\cos 20^{\circ}+\cos 30^{\circ}$
$=2 \cos ^2 5^{\circ}+2 \cos 25^{\circ} \cos 5^{\circ}$
$=2 \cos 5^{\circ}\left(\cos 5^{\circ}+\cos 25^{\circ}\right)$
$=2 \cos 5^{\circ}\left(2 \cos 15^{\circ} \cos 10^{\circ}\right)$
$=4 \cos 5^{\circ} \cos 10^{\circ} \cos 15^{\circ}$

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