If sin⁡xsin⁡y=12,cos⁡xcos⁡y=32,where x,y∈0,π2, then the value of tan (x+y) is equal to 

If sinxsiny=12,cosxcosy=32,where x,y0,π2, then the value of tan (x+y) is equal to 

  1. A

    13

  2. B

    14

  3. C

    17

  4. D

    15

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    Solution:

    Given,sinxsiny=12, cosxcosy=32

     tanxtany=13

    tan(x+y)=tanx+tany1tanxtany=4tanx13tan2x Also,  siny=2sinx, cosy=23cosx

    sin2y+cos2y=4sin2x+4cos2x9=1 36tan2x+4=9sec2x=91+tan2x 27tan2x=5 tanx=533 tan(x+y)=453311527=15

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