You are here:

Algebra/cosine question


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.


All Answers

Answers by Expert:

Ask Experts


Scott A Wilson


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.

Documents at Boeing in assistance on the manufacturiing floor.

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.

©2016 All rights reserved.