Question

sin2x-sin8x-cos10x=1

Answer 1

Ответ:

Пошаговое объяснение:

sin2x-sin8x = 2*(-sin3x)* cos5x

2*(-sin3x)* cos5x - cos^2 (5x) + sin^2 (5x) - sin^2 (5x) - cos^2 (5x) = 0

2*(-sin3x)* cos5x - 2cos^2 (5x) = 0  

sin3x * cos5x + cos^2 (5x) = 0

cos5x * (sin3x + cos5x) = 0

cos5x * (sin3x + sin(pi/2 - 5x)) = 0

cos5x * 2sin(pi/4 - x) * cos(4x - pi/4) = 0

cos5x = 0

5x = pi/2 + pin

x1 = pi/10 + pin/5, n ∈ Z

sin(pi/4 - x) = 0

pi/4 - x = pik

x2 = pi/4 - pik, k ∈ Z

cos(pi/4 + 4x) = 0

4x - pi/4 = pi/2 + pim

4x = 3pi/4 + pim

x3 = 3pi/16 + pim/4, m ∈ Z