Question

Sin²22,5°+sin22,5°×cos22,5°

Answer 1

Sin^22.5°+sin22.5 °×cos 22.5 правильно незнаю .

Answer 2

To calculate the expression sin²(22.5°) + sin(22.5°) × cos(22.5°), you can use the trigonometric identities to simplify it.

First, we need to know some basic trigonometric identities:

1. sin²θ = (1 - cos(2θ)) / 2
2. cos²θ = (1 + cos(2θ)) / 2
3. sin(2θ) = 2sin(θ)cos(θ)

Now, let's proceed with the calculation:

1. sin²(22.5°) = (1 - cos(2 × 22.5°)) / 2 = (1 - cos(45°)) / 2 = (1 - √2/2) / 2 = (2 - √2) / 4

2. sin(22.5°) × cos(22.5°) = sin(2 × 22.5°) / 2 = sin(45°) / 2 = √2/2

Now, add the two results:

sin²(22.5°) + sin(22.5°) × cos(22.5°) = (2 - √2) / 4 + √2/2

To simplify this further, let's get a common denominator for both terms:

= (2 - √2) / 4 + (2√2) / 4

Now, add the two fractions:

= (2 - √2 + 2√2) / 4 = (2 + √2) / 4

So, the simplified result is:

sin²(22.5°) + sin(22.5°) × cos(22.5°) = (2 + √2) / 4