Question

Обчислiть: sin2 54*+cos2 54* = ? (tg 60*+2 cos 45*) (√3-√2) = ? ctg 45* + 2 sin 60*tg 60* = ?

Answer 1

1) 1

2) 0.43

3) 0.42

Проверьте, правильно ли Вы написали условие)

Answer 2

To calculate the given expressions, we'll start by using some trigonometric identities. Here are the steps for each expression:

1. Calculate sin^2(54°) + cos^2(54°):

We know that sin^2(x) + cos^2(x) = 1 for any angle x.

Therefore, sin^2(54°) + cos^2(54°) = 1.

2. Calculate tg(60°) + 2 cos(45°):

Since tan(60°) = √3 and cos(45°) = √2 / 2, we can plug these values into the expression:

tg(60°) + 2 cos(45°) = √3 + 2 * (√2 / 2)

Simplifying, we get:

tg(60°) + 2 cos(45°) = √3 + √2

3. Calculate (√3 - √2) / (ctg(45°) + 2 sin(60°) * tg(60°)):

We know that cot(x) = 1 / tan(x).

Let's first calculate the denominator: ctg(45°) + 2 sin(60°) * tg(60°).

Since cot(45°) = 1, sin(60°) = √3 / 2, and tan(60°) = √3, we can plug these values into the expression:

ctg(45°) + 2 sin(60°) * tg(60°) = 1 + 2 * (√3 / 2) * √3

Simplifying, we get:

ctg(45°) + 2 sin(60°) * tg(60°) = 1 + 3 = 4

Now, let's calculate the whole expression:

(√3 - √2) / (ctg(45°) + 2 sin(60°) * tg(60°)) = (√3 - √2) / 4

So, the final value is (√3 - √2) / 4.

Remember to double-check your calculations, and always verify the results to avoid errors.