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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
if A, B, C are the angles of a triangle, then sin 2A + sin 2B - sin 2C is equal to
  • A
    4 sin A cos B cos C
  • B
    4 cos A
  • C
    4 sin A cos A
  • ✓
    4 cos A cos B sin C
✓

Answer

Correct option: D.
4 cos A cos B sin C
(D)
$\sin 2 A+\sin 2 B-\sin 2 C$
$=2 \sin A \cos A +2 \cos (B+ C ) \sin ( B - C )$
$=2 \sin A \cos A -2 \cos A \sin ( B - C )$
$=2 \cos A[\sin A -\sin ( B - C )]$
$=2 \cos A[\sin ( B + C )-\sin ( B - C )]$
$\ldots[\because \sin (B+C)=\sin A]$
$=2 \cos A(2 \cos B \sin C )$
$=4 \cos A \cos B \sin C$
Trick : Check by assuming $A = B =45^{\circ}$ and $C =90^{\circ}$

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