Question

Cos^2(35градусов) - sin^2(55градусов)

Answer 1

Решение во вложении.

Answer 2

To solve this expression, let's use the trigonometric identities for cosine and sine squared:

1. cos^2(x) = 1 - sin^2(x)
2. sin^2(x) = 1 - cos^2(x)

We can rewrite the given expression using these identities:

cos^2(35 degrees) - sin^2(55 degrees) = (1 - sin^2(35 degrees)) - (1 - cos^2(55 degrees)) = 1 - sin^2(35 degrees) - 1 + cos^2(55 degrees) = -sin^2(35 degrees) + cos^2(55 degrees)

Now we can substitute the values and calculate the expression:

• sin^2(35 degrees) + cos^2(55 degrees) = -(sin(35 degrees))^2 + (cos(55 degrees))^2

Using a calculator, we can find the values of sin(35 degrees) and cos(55 degrees):

sin(35 degrees) ≈ 0.5736 cos(55 degrees) ≈ 0.5736

Substituting these values into the expression:

• (0.5736)^2 + (0.5736)^2 = 0.3289 + 0.3289 = 0.6578

Therefore, cos^2(35 degrees) - sin^2(55 degrees) is approximately equal to 0.6578.