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27 July, 20:56

Find cos (a), if cos (a) ^4 - sin (a) ^4 = 1/8

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  1. 27 July, 21:23
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    3/4, - 3/4

    Step-by-step explanation:

    Using the difference of squares we can change things around.

    cos (a) ^4 - sin (a) ^4

    (cos^2 (a) + sin^2 (a)) ((cos^2 (a) - sin^2 (a)) then sin^2 + cos^2 = 1

    cos^2 (a) - sin^2 (a) Using the same identity sin^2 = 1 - cos^2

    cos^2 (a) - (1 - cos^2 (a))

    cos^2 (a) - 1 + cos^2 (a)

    2*cos^2 (a) - 1

    So let's use this.

    2*cos^2 (a) - 1 = 1/8

    2*cos^2 (a) = 9/8

    cos^2 (a) = 9/16

    cos (a) = + / - 3/4

    so 3/4 can be positive or negative
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