prove that 1 + cos² 2x = 2 (cos^4+ x + sin^4x ​

Question

prove that 1 + cos² 2x = 2 (cos^4+ x + sin^4x

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Isabella 1 month 2021-08-13T17:11:18+00:00 1 Answer 0 views 0

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    2021-08-13T17:12:24+00:00

    LHS:

    2[cos⁴(x) + sin⁴(x)]

    =2{[cos²(x) + sin2(x)]² − 2sin²(x).cos²(x)}

    =2[1 − 2sin²(x).cos²(x)]

    =2 − 4sin²(x)cos²(x)

    =2 − 4.[1−cos(2x)].[1+cos(2x)]

    2 2

    =2 − [1 − cos²(2x)]

    =2 + cos²(2x) − 1

    =1+cos²(2x)

    HENCE PROVED!!!

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