sin15x × sin3x+cos7x×cos11x=0. Created by Elvira0800. matematika-ru

sin15x × sin3x+cos7x×cos11x=0...

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1/2(cos(15x - 3x) - cos(15x + 3x)) + 1/2(cos(7x - 11x) + cos(7x + 11x)) = 0
1/2 cos12x - 1/2 cos18x + 1/2 cos4x + 1/2 cos18x = 0
cos12x + cos4x = 0
2cos((12x + 4x)/2)·cos((12x - 4x)/2) = 0
cos8x = 0 или cos4x = 0
8x = π/2 + πn 4x = π/2 + πk
x = π/16 + πn/8 x = π/8 + πk/4

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АртёмУмник

sin15x*sin3x+cos7x*cos11x=0

2cos(12x) - 1/2cos(4x) = 0

2*sin( 12x + 4x)/2sin(4x - 12x)/2 = 0

sin(8x) = 0

8cos=πn, n∈X

8x=(πn)/8, n∈Z

8x=(пи/4)=0

Ответ:πn/16+πn/8 и πn/4+πn/8

2 votes Thanks 1

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