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15 December, 08:32

a physicist needs to calculate the exact value of a force (measured in newtons) in the horizontal direction with the expression 25cos75. Simplify the expression to find the exact value

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  1. 15 December, 08:55
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    25*√ ((2-√3) / 2)

    Step-by-step explanation:

    Use the identity: cos (x) = sin (90°-x)

    cos (75°) = sin (90°-75°) = 25sin (90°-75°)

    Simplify

    25sin (15°)

    then write sin (15°) as sin (30°/2)

    Use the half-angle identity: sin (x/2) = ((1-cos (x)) / 2) ^ (1/2)

    ((1-cos (30°)) / 2) ^ (1/2) cos (30°) = ((3) ^ (1/2)) / 2

    then plug that in for the cos (30°) and solve

    √ ((2-√3) / 2) multiply by 25

    25*√ ((2-√3) / 2)
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