Question

1)2sin²×-sin²x 2)sin²40°+cos²40° 3)cos(3p/2+a)

Answer 1

Ответ:I hope its clear

Пошаговое объяснение:

Answer 2

Let's solve each of these trigonometric expressions one by one:

1. 2sin²x - sin²x:

To simplify this expression, we'll combine like terms. Since sin²x appears in both terms, we can factor it out:

2sin²x - sin²x = sin²x(2 - 1)

Now, simplify the constants:

sin²x(2 - 1) = sin²x(1)

Finally, any number multiplied by 1 is itself, so:

sin²x(1) = sin²x

So, the simplified form of 2sin²x - sin²x is sin²x.

2. sin²40° + cos²40°:

This expression represents the trigonometric identity known as the Pythagorean Identity, which states that for any angle θ:

sin²θ + cos²θ = 1

In this case, θ is 40 degrees. So, using the Pythagorean Identity:

sin²40° + cos²40° = 1

So, the value of sin²40° + cos²40° is 1.

3. cos(3π/2 + α):

To find the value of cos(3π/2 + α), we need to consider the properties of the cosine function. In particular, we can use the angle sum formula for cosine, which is:

cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

In this case, A = 3π/2 and B = α. So, substituting these values into the formula:

cos(3π/2 + α) = cos(3π/2)cos(α) - sin(3π/2)sin(α)

Now, let's determine the values of cos(3π/2) and sin(3π/2):

cos(3π/2) = 0 (cosine is 0 at 3π/2) sin(3π/2) = -1 (sine is -1 at 3π/2)

So, the expression becomes:

cos(3π/2 + α) = 0 * cos(α) - (-1) * sin(α)

Simplify further:

cos(3π/2 + α) = 0 + sin(α)

Therefore, the value of cos(3π/2 + α) is sin(α).