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    alshattii94's Avatar
    alshattii94 Posts: 2, Reputation: 1
    New Member
    		  
    #1

    Oct 23, 2013, 05:07 AM
    Using the trigonometric identities, prove the educatiuon
    sin2 x sin 5x + cos 2x cos 5x = cos 3x
    this the education please help me because I have an assignment
    Celine91's Avatar
    Celine91 Posts: 51, Reputation: 9
    Junior Member
    		  
    #2

    Oct 23, 2013, 05:52 AM
    simply use the formula: cos(A+B) = cos(A)cos(B) - sin(A)sin(B)

    in your question let A = 5x and B = -2x (because 5x - 2x = 3x)

    so cos (5x+ (-2x)) = cos(5x)cos(-2x) - sin(5x)sin(-2x)
    where, cos(-2x) = cos(2x) and sin(-2x) = - sin(2x)

    Simply substitute in the above equation you get:

    cos (5x + (-2x)) = cos(5x)cos(2x) + sin(5x)sin(2x)
    ==> cos (3x) = sin(2x)sin(5x) + cos(2x)cos(5x)

    (to prove equality start with the simpler side and expand)
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