Question

I need Trig Identity help please..! (Grade 12)

How do I prove...

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

Answer 1

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

Answer 2

Ohhhhh you are right my mistake!

Answer 3

It should be

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

hmm

Answer 8

im still stuck :(

Answer 9

I THINK I GOT IT :)

Answer 10

yay double angles worked~~~!!

Answer 11

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.

Answer 12

@pottersheep do you need hint?