In a △ABC,a+ca−ctan⁡B2 is equal to

In a ABC,a+cactanB2 is equal to

  1. A

    tanB2+C

  2. B

    tanB+C2

  3. C

    cotB2+C

  4. D

    none of these

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    Solution:

    Using sine rule, we have

    a+cactanB2=sinA+sinCsinAsinCtanB2 a+cactanB2=2sinA+C2cosAC22sinAC2cosA+C2tanB2 a+cactanB2=cosB2cosAC2sinAC2sinB2tanB2 a+cactanB2=cotAC2 a+cactanB2=cotπBCC2 [A+B+C=π] a+cactanB2=tanB2+C

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