Задача 71279 sqrt(2) - 2sqrt(2)sin^2 9Pi/8 ...

645763d493fd565c85034d5b

07.05.2023 11:43:53

sqrt(2) - 2sqrt(2)sin^2 9Pi/8

5f3ea7e3faf909182968ddd9

07.05.2023 14:15:55

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[m]sin\frac{9π}{8}=sin(π+\frac{π}{8})=-sin\frac{π}{8}[/m]

[m]\sqrt{2}-2\sqrt{2}sin^2\frac{9π}{8}=\sqrt{2}-2\sqrt{2}sin^2\frac{π}{8}=\sqrt{2}\cdot (1-2sin^2\frac{π}{8})=[/m]


[m]=\sqrt{2}\cdot (\underbrace{cos^2\frac{π}{8}+sin^2\frac{π}{8}}_{1}-2sin^2\frac{π}{8})=\sqrt{2}\cdot (cos^2\frac{π}{8}-sin^2\frac{π}{8})=\sqrt{2}\cdot cos\frac{2π}{8}=\sqrt{2}\cdot cos\frac{π}{4}=\sqrt{2}\cdot \frac{\sqrt{2}}{2}=1[/m]