- #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 FAQ: Solve cosx^4-sinx^4: Confirm My Answer?
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.
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.
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.
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.
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).