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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
If $A + B + C =\pi$, then $\cos 2A+\cos 2B+\cos 2C=$
  • A
    1 + 4 cos A cos B sin C
  • B
    - 1 + 4 sin A sin B cos C
  • ✓
    - 1 - 4 cos A cos B cos C
  • D
    1 + 4 sin A sin B sin C
✓

Answer

Correct option: C.
- 1 - 4 cos A cos B cos C
(C)
\[\cos 2 A+\cos 2 B+\cos 2 C\]
$=2 \cos (A+ B ) \cos ( A - B )+\left(2 \cos ^2 C -1\right)$
$=-1-2 \cos C \cos (A-B)+2 \cos ^2 C$$\ldots[\because \cos (A+B)=-\cos C]$
$=-1-2 \cos C [\cos ( A - B )+\cos ( A + B )]$
$=-1-4 \cos A \cos B \cos C$

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