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Mathematics
27 February, 12:08
How would you solve cos (5x) = sin (10x) ?
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Oliver Cuevas
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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