Multiple Choice Questions on If A B C 180 deg then what is sin 2A ndash sin 2B ndash sin 2C equal to ........ for NDA Exam Preparation

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Multiple Choice Questions

If A B C 180 deg then what is sin 2A ndash sin 2B ndash sin 2C equal to ........

Mathematics (NDA) Trigonometry
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    If A + B + C = 180°, then what is sin 2A – sin 2B – sin 2C equal to?

     

    –4 sin A sin B sin C

    Incorrect Answer

     –4 cos A sin B cos C

    Incorrect Answer

    –4 cos A cos B sin C

    Incorrect Answer

    –4 sin A cos B cos C

    Correct Answer
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    Explanation:
    sin2A−sin2B−sin2C
    =2cos(A+B)⋅sin(A−B)+sin(2A+2B)
    =2cos(A+B)sin(A−B)+2sin(A+B)cos(A+B)
    =2cos(A+B)[sin(A−B)+sin(A+B)]
    =−2cosC[2sinA⋅cosB]
    =−4sinAcosBcosC

    By: Munesh Kumari
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