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JEE Main & Advanced Mathematics Triangles & Properties of Triangle Question Bank Self Evaluation Test - Properties of Triangles and Height & Dstances

  • question_answer
    If \[A+B+C=\pi ,\] then\[\cos 2A+\cos 2B+\cos 2C+4\sin A\sin B\sin C\] is equal to:

    A) 0

    B) 1

    C) 2

    D) 3

    Correct Answer: B

    Solution :

    [b] If \[A+B+C=\pi ,\] then \[\cos mA+\cos mB+\cos mC\] \[=1-4\sin \frac{mA}{2}\sin \frac{mB}{2}\sin \frac{mC}{2}\] \[\therefore \] For \[m=2:\cos 2A+\cos 2B+\cos 2C\] \[=1-4\sin A\sin B\sin C\] \[\Rightarrow \cos 2A+\cos 2B+\cos 2C\] \[+4\sin A\sin B\operatorname{sinC}=1\]


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