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27 February, 12:08

How would you solve cos (5x) = sin (10x) ?

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  1. 27 February, 12:18
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    We will use double angle identities:

    cos (5x) = sin (10x)

    cos (5x) = 2 cos (5x) sin (5x)

    cos (5 x) - 2 cos (5 x) sin (5x) = 0

    cos (5 x) · [ 1 - 2 sin (5 x) ] = 0

    cos (5 x) = 0 or : 1 - 2 sin (5 x) = 0

    5 x = π/2 + kπ, k∈Z sin (5 x) = 1/2

    x1 = π/10 + kπ/5 5 x = π/6+2kπ, k∈ Z

    5 x = 5π/6 + 2kπ, k∈ Z

    x 2 = π/30 + 2kπ/5

    x 3 = π/9 + 2kπ/5
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