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7 April, 05:34

Find the exact value of tan (x-y) if sinx=8/17 and cosy=3/5

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  1. 7 April, 09:20
    0
    To solve the the question we proceed as follows:

    From trigonometric laws

    (cos x) ^2 + (sin x) ^2=1

    (cos y) ^2 + (sin y) ^2=1

    sin (x-y) = sin x sin y-sin y cos x

    cos (x-y) = cos x cos y + sin x sin y

    si x=8/17

    cos x=sqrt (1 - (sin x) ^2) = sqrt (1-64/289) = sqrt (225/289) = 15/17

    cos y=3/5

    sin x = sqrt (1 - (cos x) ^2) = sqrt (1-9/25) = sqrt (16/25) = 4/5

    thus

    tan (x-y) = [sin (x-y) ]/[cos (x-y) ]

    =[sin x cos y-sin y cos x]/[cos x cos y+sin x sin y]

    plugging in the values we obtain:

    [8/17 * 3/5-4/5*15/7]/[15/17*3/5+8/17*4/5]

    simplifying

    [24/85-60/85]/[45/85+32/85]

    =-36/77
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