- #1
synergix
- 178
- 0
Homework Statement
simplify cosx4-sinx4
The Attempt at a Solution
I got cos2x
does anybody want to solve this and let me know if I am right ?
Solve cosx^4-sinx^4: Confirm My Answer?
- Thread starter synergix
- Start date
In summary, the expression cosx^4-sinx^4 can be simplified to 1-cos2x using the identity cos^2x-sin^2x = 1. It has a degree of 4 and can be confirmed by plugging in values or graphing. It can also be written as 2cos^2(2x) using the double angle formula for cosine. Furthermore, it can be factored as (1+cos2x)(1-cos2x) using the difference of squares formula.
simplify cosx4-sinx4
I got cos2x
does anybody want to solve this and let me know if I am right ?
- #2
srvs
- 31
- 0
Cos2x is correct.
- #3
tiny-tim
Science Advisor
Homework Helper
- 25,839
- 258
synergix said:
Hi synergix!
It's obviously cos2x
…if you're not sure, then either you didn't go the quick way (factorise a4 - b4
), or you're not familiar enough with your trignonometric identities 1. How do you solve cosx^4-sinx^4?
The expression cosx^4-sinx^4 can be simplified using the identity cos^2x-sin^2x = 1. This can be rewritten as (cos^2x)^2 - (sin^2x)^2, which is a difference of squares. Using the formula a^2-b^2 = (a+b)(a-b), we get (cos^2x+sin^2x)(cos^2x-sin^2x). The first term simplifies to 1, and the second term is equal to cos2x. Therefore, the final answer is 1-cos2x.
2. What is the degree of the polynomial in cosx^4-sinx^4?
The degree of the polynomial in cosx^4-sinx^4 is 4. This is because both cosx^4 and sinx^4 have a degree of 4, and when you subtract them, the highest degree term that remains is also 4.
3. Can you confirm my answer for cosx^4-sinx^4?
Yes, I can confirm your answer for cosx^4-sinx^4 by plugging in specific values for x and checking if the answer matches. You can also use a graphing calculator to graph both sides of the equation and see if they intersect at the same points, indicating that they are equal.
4. Is there another way to write cosx^4-sinx^4?
Yes, there is another way to write cosx^4-sinx^4. Using the double angle formula for cosine, we can rewrite cosx^4-sinx^4 as 2cos^2(2x). This form may be more useful in certain situations, such as when solving for x.
5. Can the expression cosx^4-sinx^4 be factored?
Yes, the expression cosx^4-sinx^4 can be factored using the difference of squares formula as mentioned in the first question. The factored form is (1+cos2x)(1-cos2x).
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