Question

Sin²α-cos²α=помогите решить

Answer 1

Cos^2a - sin^2a = cos2a (формула двойного угла)
... = - (cos^2a - sin^2a) = -cos2a

Answer 2

Sure, I can help you solve the equation: sin²α - cos²α = 0.

To solve this trigonometric equation, we can use the trigonometric identity: sin²α - cos²α = sin²α - (1 - sin²α) = 2sin²α - 1.

So, the equation becomes: 2sin²α - 1 = 0.

Now, we want to isolate sin²α on one side of the equation:

2sin²α = 1.

Divide both sides by 2:

sin²α = 1/2.

Now, to find the values of α, we can take the square root of both sides:

sinα = ±√(1/2).

We can find the angles using the unit circle or a calculator. The two solutions for α are:

1. α = arcsin(√(1/2)) ≈ 45 degrees.
2. α = π - arcsin(√(1/2)) ≈ 135 degrees (or α ≈ 180 - 45 ≈ 135 degrees in the second quadrant).

Keep in mind that there are multiple solutions to this equation, as trigonometric functions are periodic. So, there are infinitely many angles α that satisfy the original equation.