Question

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Answer 1

35.
sin5x - sin3x = 0
2 * sin((5x-3x)/2) * cos((5x+3x)/2) = 0
2 * sinx * cos4x = 0

sinx = 0
cos4x = 0

x = πn
4x = π/2 + πn

x = πn
x = π/8 + πn/4
n ∈ Z

36.
cos4xcos5x + sin4xsin5x = √3/2
cos(5x - 4x) = √3/2
cosx = √3/2

x = π/6 + 2πn
x = -π/6 + 2πn
n ∈ Z