## pottersheep 3 years ago I need Trig Identity help please..! (Grade 12) How do I prove... (cos2x/1+sin2x) = tan(pi/4- x)

1. tkhunny

You have written this: $$\dfrac{\cos(2x)}{1} + \sin(2x) = \tan(\frac{\pi}{4} - x)$$. Is this what you intend?

2. pottersheep

Ohhhhh you are right my mistake!

3. pottersheep

It should be (cos2x/(1+sin2x) = tan(pi/4- x)

4. anonymous

$\frac{\cos^2(x)}{1+\sin^2(x)}$?

5. pottersheep

No, They are not to the power of 2, they are just 2x :)

6. tkhunny

Well, it certainly looks like an exercise in double angles. Perhaps expanding all three expressions will lead to something.

7. pottersheep

hmm

8. pottersheep

im still stuck :(

9. pottersheep

I THINK I GOT IT :)

10. pottersheep

yay double angles worked~~~!!

11. tkhunny

Let's see your work and perhaps we can untangle it. $$\cos(2x) = \cos^{2}(x) - \sin^{2}(x) = 1 - 2\sin^{2}(x) = 2\cos^{2}(x) - 1$$ $$\sin(2x) = 2\sin(x)\cos(x)$$ You may wish to convert the tangent to sine/cosine. Really, the idea behind these things is to get you to EXPLORE these relationships. Don't expect to see a clear solution right away. Play with it until somthing pops out.

12. sirm3d

@pottersheep do you need hint?