Help with Trig Function: Sec(2x)csc(x)sin(2x) and C=cosx

[Mark53]

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]

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.

 

[ehild]

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?

So you got $\frac{1}{\cos^2(x)-\sin^2(x)}\frac{1}{\sin(x)}2\sin(x)\cos(x)=\frac{2sin(x)\cos(x)}{(\cos^2(x)-\sin^2(x))\sin(x)}$

Why don't you simplify with sin(x)?

 

[Mark53]

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.

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?

 

[Mark53]

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?

made a mistake it should be

2C/(2C^2-1)

 

[ehild]

made a mistake it should be

2C/(2C^2-1)

Finally, that is correct.