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Math Help - trig question

  1. #1
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    trig question

    show that (sin A + cos A) (Sin B + Cos B)= Sin (A +B) + Cos (A-B)
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  2. #2
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    Quote Originally Posted by dane View Post
    show that (sin A + cos A) (Sin B + Cos B)= Sin (A +B) + Cos (A-B)
     RHS = \sin(A+B) + \cos(A-B)

    Expand both of these:

     =\sin(A)\cos(B)+\sin(B)\cos(A) + \cos(A)\cos(B) + \sin(A)\sin(B)

    Now factor out sin(A) and cos(A) from the relevant expressions:

     =\sin(A)(\cos(B)+\sin(B)) + \cos(A)(\sin(B) + \cos(B))

    Now realise that the inside of the brackets of both sides are identical. Hence the expression in the brackets is a factor of both terms. Take it our as a factor:

     =(\cos(B)+\sin(B))(\sin(A)+\cos(A)) = LHS
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