Question

Cos^{2} ( alpha - 3/2 pi ) =  ?

Answer 1

Cos^2(a-3/2pi)=cos^2(3/2pi-a)=sin^2a

Answer 2

To solve this equation, let's break it down step by step:

First, let's simplify the expression inside the cosine function: alpha - (3/2)π

We know that cosine is a periodic function with a period of 2π. Therefore, we can add or subtract any multiple of 2π to the angle without changing the value of the cosine function.

In this case, we have an angle of (3/2)π, which is equivalent to an angle of π/2. So we can rewrite the expression as follows:

α - (3/2)π = α - π/2

Now, let's rewrite the equation using the simplified expression:

cos^2(α - π/2)

Since cosine is an even function, cos(θ) = cos(-θ). Therefore, cos^2(α - π/2) is equivalent to cos^2(π/2 - α).

Now we have:

cos^2(π/2 - α)

Using the identity cos^2(θ) = sin^2(π/2 - θ), we can rewrite the expression as:

sin^2(α)

So, cos^2(α - (3/2)π) is equal to sin^2(α).