Question

Sin^4+cos^2-cos^4/////

Answer 1

Sin^4+cos^2-cos^4=(sin^2+cos^2)(sin^2-cos^2) + cos^2= cos^2+(sin^2-cos^2)= ((1-cos2)/2) + (sin^2-cos^2)

Answer 2

It looks like you want to simplify the expression:

sin^4 + cos^2 - cos^4

Let's break this down step by step:

1. Start with the terms involving sine and cosine: sin^4 - cos^4 + cos^2

2. Now, notice that sin^4 - cos^4 is a difference of squares. You can factor it as follows: (sin^2 + cos^2)(sin^2 - cos^2) + cos^2

3. Remember that sin^2 + cos^2 is equal to 1 (due to the Pythagorean trigonometric identity), so we can substitute that in: (1)(sin^2 - cos^2) + cos^2

4. Now, recognize that sin^2 - cos^2 can be expressed as the difference of squares: (1)(sin + cos)(sin - cos) + cos^2

5. Multiply the constants and simplify: sin + cos - cos + cos^2

6. Combine like terms: sin + cos^2

So, the simplified expression is sin + cos^2.