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

1. tkhunny Group Title

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

2. pottersheep Group Title

Ohhhhh you are right my mistake!

3. pottersheep Group Title

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

4. satellite73 Group Title

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

5. pottersheep Group Title

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

6. tkhunny Group Title

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

7. pottersheep Group Title

hmm

8. pottersheep Group Title

im still stuck :(

9. pottersheep Group Title

I THINK I GOT IT :)

10. pottersheep Group Title

yay double angles worked~~~!!

11. tkhunny Group Title

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 Group Title

@pottersheep do you need hint?