Предмет: Алгебра, автор: xzloyx

Решите уравнение
cosxsin9x=cos3xsin7x

Ответы

Автор ответа: pavlikleon

3

$sin \alpha cos \beta = \frac{sin( \alpha + \beta)+sin( \alpha - \beta ) }{2}$

$\frac{1}{2}( sin(9x+x)+sin(9x-x))= \frac{1}{2} (sin(3x+7x)+sin(7x-3x)), \\ sin(9x+x)+sin(9x-x)=sin(3x+7x)+sin(7x-3x), \\ sin10x +sin8x=sin10x+sin4x, \\ sin8x=sin4x \\ 2sin4xcos4x=sin4x \\ sin4x=0, 2cos4x=1 \\ 4x= \pi n, \\ x= \frac{ \pi }{4}n \\ cos4x= \frac{1}{2} \\ 4x=+- \frac{ \pi }{3}+2 \pi k \\ x=+-\frac{\pi}{12}+\frac{\pi k}{2}$
Ответ:
х∈{πn/4;-π/12+πn/2; π/12+πn/2}, n∈Z

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ЗАДАНИЕ № 13.

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3. The territory of the UK is rather large.

4. Great Britain is one the most densely populated countries in the world.

5. There are 2 official languages in the UK.

6. Great Britain is a country with new traditions and customs.

7. The UK is one of the most highly developed industrial counties in the world.

8. This country is the world largest producer of different machinery and electronics.

9. The capital of the country, London, is one of the world largest ports.

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