You are here:

- Home
- Science
- Math for Kids
- Algebra
- cosine question

Advertisement

Hello Scott,

I really need help with this question. I've gone through all of what I know, but I just can't figure it out.

Note: x is used for theta

Write the expression in terms of cos(x). Then, simplify.

cos^4x - sin^4x + sin^2x

Thank you!

The expression cos^4(x) - sin^4(x) + sin^2(x) can be rewritten as

cos^4(x) - sin^2(x)(sin^2(x) - 1).

Since it is known that sin^2(x) + cos^2(x) = 1,

we can say that -sin^2(x) = cos^2(x) - 1 and sin^2(x) - 1 = -cos^2(x).

Putting these into cos^4(x) - sin^2(x)(sin^2(x) - 1) gives

cos^4(x) + (cos^2(x) - 1)(-cos^2(x)).

Multiplying this out gives cos^4(x) - cos^4(x) + cos^2(x).

The first two terms cancel, leaving only cos^2(x).

Another approach would be to factor the original into

(cos^x(2) - sin^2(x))(cos^2(x) + sin^2(x)) + sin^2(x).

It is known that cos^2(x) + sin^2(x) = 1, so we have

cos^2(x) - sin^2(x) + sin^2(x).

Here, the sin^2(x) terms cancel, leaving cos^2(x).

Either way, there's the answer.

- Add to this Answer
- Ask a Question

Rating(1-10) | Knowledgeability = 10 | Clarity of Response = 10 | Politeness = 10 |

Comment | Perfect and a very clear, concise answer. Thanks! |

Algebra

Answers by Expert:

Any algebraic question you've got. That includes question that are linear, quadratic, exponential, etc.

I have solved story problems, linear equations, parabolic equations.
I have also solved some 3rd order equations and equations with multiple variables.
**Publications**

Documents at Boeing in assistance on the manufacturiing floor.**Education/Credentials**

MS at math OSU in mathematics at OSU, 1986.
BS at OSU in mathematical sciences (math, statistics, computer science), 1984.
**Awards and Honors**

Both my BS and MS degrees were given with honors.
**Past/Present Clients**

Students in a wide variety of areas since the 80's; over 1,000 of them have been in algebra.