Can you provide the solution?

Question

Hellllllllp please. Here is the problem:

Simplify the trigonometric expression.

sin⁴(𝛼) − cos⁴(𝛼) + cos²(𝛼)

What is the solution?

Answer 1

Do you know how to factor x⁴ - y⁴?

That is a difference of squares, so it factors like this:

(x² - y²)(x² + y²).

Do the same for sin⁴(α) - cos⁴(α).

Then realize that there is a Pythagorean Trigonometric Identity that allows you to replace sin²(α) + cos²(α) with the value 1. From there simplify and combine similar terms and you will have your answer.