Titandwedebil said:Okay, so I thought that maybe (cos4x) + (sin4x) might be the same as its Pythagorean identity (which would make that mess just "1"
dextercioby said:Think of (a+b)^2 expansion...
Titandwedebil said:What's that?
Titandwedebil said:Homework Statement
(cos4x) + 2(cos2x)(sin2x) + (sin4x)
Homework Equations
All Pythagorean, reciprocal, and quotient identities.
The Attempt at a Solution
Okay, so I thought that maybe (cos4x) + (sin4x) might be the same as its Pythagorean identity (which would make that mess just "1"; giving me...
2(cos2x)(sin2x) + 1
From there I haven't the slightest idea on what to do. The answer to this one is supposed to be just "1".
That looks like the hard way to do it! DexterCioby's idea is best.Ray Vickson said:Write s = sin(x) and note that cos^2(x) = 1-s^2, so you have (1-s^2)^2 + 2*(1-s^2)*s^2 + s^4. Expand it out.
RGV
Simplifying equations allows us to better understand the relationships between different variables and to solve problems more efficiently. It also makes the equation easier to work with and reduces the chances of making errors.
An equation can be simplified when there are terms that can be combined or canceled out, and when the equation can be written in a more compact and organized form. This usually involves using the rules of algebra, such as the distributive property, to simplify the equation.
Some common techniques for simplifying equations include factoring, combining like terms, using the distributive property, and canceling out common factors. It is also helpful to have a good understanding of basic algebraic operations and their properties.
No, simplifying an equation does not change its solution. Simplifying only involves rearranging and organizing the terms in the equation, but the overall value of the equation remains the same. Therefore, the solution to the simplified equation will be the same as the solution to the original equation.
Yes, there are some general rules and guidelines for simplifying equations, such as always working in the correct order of operations, being careful with negative signs, and checking for common factors. It is also important to pay attention to any restrictions or special cases that may apply to the equation.