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Math10
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Homework Statement
How to simplify 1-2*sqrt(x)*sin(sqrt(x))*cos(sqrt(x))?
Homework Equations
None.
The Attempt at a Solution
I know the identity that sin(2x)=2sin(x)cos(x).
Or sin(2A) = 2sin(A)cos(A).Math10 said:Homework Statement
How to simplify 1-2*sqrt(x)*sin(sqrt(x))*cos(sqrt(x))?
Homework Equations
None.
The Attempt at a Solution
I know the identity that sin(2x)=2sin(x)cos(x).
Math10 said:So it's 1-Asin(2A)?
But what is A? There is no A in the original problem.Math10 said:1-Asin(2A).
Right. So now replace A by ##\sqrt{x}##.Math10 said:You said to let A=sqrt(x). See what you posted above.
It's easy enough to check whether this is equal to what you started with.Math10 said:So 1-sqrt(x)*sin(2*sqrt(x)).
To simplify an equation, you need to combine like terms, use the distributive property, and follow the order of operations. This will help you to get rid of any unnecessary terms and make the equation easier to solve.
Yes, you can simplify expressions with variables by grouping like terms, combining coefficients, and using the properties of exponents. The goal is to get the expression in its simplest form, with no more than one variable term.
One common mistake to avoid is forgetting to distribute negative signs or coefficients when using the distributive property. Another mistake is not following the correct order of operations, which can change the answer. It is also important to double-check your answer by plugging it back into the original equation.
An expression is fully simplified when all like terms are combined, there are no parentheses left to distribute, and the coefficients are as small as possible. The variables should also be in alphabetical order, and there should be no more than one variable term.
Yes, there are certain rules and properties that you can use to simplify expressions faster. For example, the commutative and associative properties allow you to rearrange terms and group them in different ways without changing the answer. It is important to learn and understand these rules to simplify expressions efficiently.