Question

Корень из2-2*Корень из2*sin^2(3pi/8)

Answer 1

Ответ:

Объяснение:

$\sqrt{2}-2\sqrt{2sin^2(\frac{3\pi}{8}) }=\sqrt{2}-2\sqrt{2\cdot\frac{1-cos(\frac{3\pi}{4}) }{2} }=\sqrt{2}-2\sqrt{1-(-\frac{\sqrt{3}}{2}) } }=\sqrt{2}-2\sqrt{1+\frac{\sqrt3}{2} }=\sqrt{2}-2\sqrt{\frac{2+\sqrt3}{2} } =\sqrt{2}-\frac{2\sqrt{2+\sqrt{3} } }{\sqrt2}=\sqrt{2}- \frac{2\sqrt{2+\sqrt3}\sqrt2 }{2}=\sqrt2-\sqrt{4+2\sqrt{3} }=\sqrt{2} -\sqrt{(1+\sqrt3)^2} =\sqrt2-|1+\sqrt3| =\sqrt2-\sqrt3-1.$

Answer 2

Ответ во влвожении Объяснение:

Answer 3

To simplify the given expression, let's start by calculating the value of each term step by step:

1. Calculate the value of square root of 2: √2 ≈ 1.41421356.
2. Calculate the value of sine squared of (3π/8) using a calculator: sin^2(3π/8) ≈ 0.85355339.
3. Calculate the square root of the result from step 2: √(0.85355339) ≈ 0.92401774.

Now, we can rewrite the original expression with the calculated values:

√2 - 2 * √2 * √(sin^2(3π/8))

Substitute the calculated values:

1.41421356 - 2 * 1.41421356 * 0.92401774

Now, perform the multiplication:

1.41421356 - 2.82842712 * 0.92401774

Calculate the multiplication:

1.41421356 - 2.61421356

Finally, calculate the subtraction:

Result ≈ -1.19999999994

So, the simplified value of the expression is approximately -1.2.