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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
$\sin 18^{\circ} \sin 70^{\circ}+\sin 16^{\circ} \sin 36^{\circ}=$
  • ✓
    $\sin 54^{\circ} \sin 34^{\circ}$
  • B
    $\sin 54^{\circ} \cos 34^{\circ}$
  • C
    $\cos 54^{\circ} \sin 34^{\circ}$
  • D
    $\cos 54^{\circ} \cos 34^{\circ}$
✓

Answer

Correct option: A.
$\sin 54^{\circ} \sin 34^{\circ}$
(A)
$\sin 18^{\circ} \sin 70^{\circ}+\sin 16^{\circ} \sin 36^{\circ}$
$=\frac{1}{2}\left[2 \sin 18^{\circ} \sin 70^{\circ}+2 \sin 16^{\circ} \sin 36^{\circ}\right]$
$=\frac{1}{2}\left[\cos 52^{\circ}-\cos 88^{\circ}+\cos 20^{\circ}-\cos 52^{\circ}\right]$
$=\frac{1}{2}\left[\cos 20^{\circ}-\cos 88^{\circ}\right]$
$=\frac{1}{2}\left[2 \sin 54^{\circ} \sin 34^{\circ}\right]$
$=\sin 54^{\circ} \sin 34^{\circ}$

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