Question

Cos^2 10 градус-sin^2 10 градус

Answer 1

Ответ:

cos(20°)

Объяснение:

С помощью формулы cos(t)²-sin(t)²=cos(2*t) мы сокращаем данное выражение до cos(2*10°) = cos(20°)

Answer 2

To simplify the expression cos^2 10 degrees - sin^2 10 degrees, we can use the trigonometric identity known as the Pythagorean identity, which states that sin^2θ + cos^2θ = 1 for any angle θ.

Let's rewrite the expression using the Pythagorean identity:

cos^2 10 degrees - sin^2 10 degrees = (1 - sin^2 10 degrees) - sin^2 10 degrees = 1 - 2sin^2 10 degrees

Now, we need to find the value of sin^2 10 degrees. Using a calculator or a trigonometric table, we can determine that sin 10 degrees ≈ 0.17364818.

Now, we substitute this value into the expression:

1 - 2(0.17364818)^2 = 1 - 2(0.0301537) = 1 - 0.0603074 = 0.9396926

Therefore, cos^2 10 degrees - sin^2 10 degrees ≈ 0.9396926.