The discussion centers around simplifying the expression 1-2*sqrt(x)*sin(sqrt(x))*cos(sqrt(x)), which involves trigonometric identities and algebraic manipulation.
Participants are actively engaging with the problem, exploring the implications of their substitutions and identities. Some have expressed uncertainty about the correctness of their transformations, while others are confirming steps taken in the simplification process.
There is a mention of a mistake found by one participant, indicating that the problem may have had additional complexities or misunderstandings that were clarified during the discussion.
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)).