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29 August, 13:41

Rewrite the given function as an equivalent function containing only cosine terms raised to a power of 1. f (x) = - 4sin^2 (x)

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  1. 29 August, 15:30
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    We have been given the following function:

    f (x) = - 4sin² (x)

    By Pythagorean identity:

    sin²x + cos²x = 1. Using this in the function given above:

    f (x) = - 4 (1 - cos²x)

    ⇒f (x) = - 4 + 4cos²x

    By half angle identity:

    cos²x = 1/2[1-cos (2x) ]

    Using this in the function above:

    ⇒f (x) = - 4 + 4 (1/2[1-cos (2x) ])

    ⇒f (x) = - 4 + 2[1 - cos (2x) ]

    ⇒f (x) = - 4 + 2 - 2cos (2x)

    ⇒f (x) = - 2 - 2cos (2x)

    ⇒f (x) = - 2[1 + cos (2x) ]
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