The discussion revolves around rewriting the expression sec(2x)csc(x)sin(2x) in terms of C, where C is defined as cos(x). Participants are exploring trigonometric identities and simplifications to express the function solely in terms of C.
Some participants have provided guidance on how to proceed with the simplification and substitution process. There is an ongoing exploration of different forms of the expression, and while some participants express confidence in their results, there is no explicit consensus on the final answer.
Participants are working under the assumption that they must express everything in terms of C, and there are indications of potential errors in calculations that are being addressed throughout the discussion.
Mark53 said:Homework Statement
Let C=cosx. Write sec(2x)csc(x)sin(2x) as a function of C.
The Attempt at a Solution
Am I on the right track
1/cos(2x) * 1/sin(x) * 2sin(x)cos(x)
1/(cos^2(x)-sin^2(x)) * `1/(sqrt(1-cos^2(x)) * 2(sqrt(1-cos^2(x))cos(x)
What would i do from here?
andrewkirk said:There is one ##\sin x## left in your formula that you need to convert to only using ##\cos x##.
Having done that, you only need to replace every ##\cos x## by ##C##, then simplify as much as possible.
Mark53 said:1/(cos^2(x)-sin^2(x)) * `1/(sqrt(1-cos^2(x)) * 2(sqrt(1-cos^2(x))cos(x)
1/(cos^2(x)-(1-cos^2(x) * 1/(sqrt(1-cos^2(x)) * 2(sqrt(1-cos^2(x))cos(x)
simplifying this I get
1/(cos(x)-1)
=1/(C-1)
Is this the correct answer?
Finally, that is correct.Mark53 said:made a mistake it should be
2C/(2C^2-1)