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8 June, 01:26

Sin = 5/13, and cos b = 3/5, evaluate cos (a-b).

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  1. 8 June, 02:40
    0
    cos (a - b) is 56/65

    Step-by-step explanation:

    Step 1:

    Given sin a = 5/13, find cos a.

    sin a = opposite side/hypotenuse = 5/13

    The adjacent side can be found using Pythagoras Theorem.

    Hypotenuse² = Opposite Side² + Adjacent Side²

    ⇒ Adjacent side² = Hypotenuse² - Opposite Side²

    = 13² - 5² = 169 - 25 = 144

    ∴ Adjacent Side = 12

    ⇒ cos a = adjacent side/hypotenuse = 12/13

    Step 2:

    Given cos b = 3/5, find sin b.

    cos b = adjacent side/hypotenuse = 3/5

    The opposite side can be found using Pythagoras Theorem.

    Hypotenuse² = Opposite Side² + Adjacent Side²

    ⇒ Opposite side² = Hypotenuse² - Adjacent Side²

    = 5² - 3² = 25 - 9 = 16

    ∴ Opposite Side = 4

    ⇒ sin b = opposite side/hypotenuse = 4/5

    Step 3:

    Find cos (a - b).

    cos (a - b) = cos a cos b + sin a sin b

    = 12/13 * 3/5 + 5/13 * 4/5

    = 36/65 + 20/65 = 56/65
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