Question

sin5x-sin3x=0
найти в градусах​

Answer 1

$sin5x - sin3x = 0\\2sin(\frac{5x + 3x}{2})cos(\frac{5x - 3x}{2}) = 0\\2sin4xcosx = 0\\sin4x_1 = 0\\4x_1 = \pi k\\x_1 = \frac{\pi }{4}k\\cosx_2 = 0\\x_2 = \frac{\pi }{2} + \pi k$

(π/4)k ∪ (π/2) + πk  =  (π/4)k = k45°

k ∈ Z

Ответ: k45°, k ∈ Z