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26 July, 10:07

Find sin (A-B) if sin A = 4/5 with A between 90 and 180 and if cos B = 3/5 with B between 0 and 90

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  1. 26 July, 10:30
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    sin (A-B) = 24/25

    Step-by-step explanation:

    The trig identity for the differnce of angles tells you ...

    sin (A - B) = sin (A) cos (B) - sin (B) cos (A)

    We are given that sin (A) = 4/5 in quadrant II, so cos (A) = - √ (1 - (4/5) ^2) = - 3/5.

    And we are given that cos (B) = 3/5 in quadrant I, so sin (B) = 4/5.

    Then ...

    sin (A-B) = (4/5) (3/5) - (4/5) (-3/5) = 12/25 + 12/25 = 24/25

    The desired sine is 24/25.
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