The value of sin⁡(B+A)+cos⁡(B−A)sin⁡(B−A)+cos⁡(B+A) is equal to

The value of sin(B+A)+cos(BA)sin(BA)+cos(B+A) is equal to

  1. A

    cosB+sinBcosBsinB

  2. B

    cosA+sinAcosAsinA

  3. C

    cosAsinAcosA+sinA

  4. D

    None of these

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    Solution:

    =sin(B+A)+cos(BA)sin(BA)+cos(B+A)=sin(B+A)+sin90BAsin(BA)+sin90B+A=2sinA+45cos45B2sin45Acos45B=sinA+45sin45A=12sinA+12cosA12cosA-12sinA=cosA+sinAcosAsinA

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