## anonymous 4 years ago (cos^4x−sin^4x)/(1−tan^4x)=cos^4x trig identity?

1. anonymous

$(\cos^4x−\sin^4x)/(1−\tan^4x)=\cos^4x$

2. anonymous

how do you prove this? :/

3. anonymous

i would start by factoring the numerator, and then see that one of the factors is 1. that should make the rest easier

4. myininaya

you can factor Mr. Denominator as well

5. anonymous

i've tried that. i've went $(\cos^2x+\sin^2x)(\cos^2x-\sin^2x)/(1-(\sin^4x/\cos^4x))$

6. myininaya

cos^2(x)+sin^2(x)=1

7. TuringTest

you don't need to get it all into sin and cos

8. myininaya

cos^2(x)-sin^2(x)=cos(2x)

9. anonymous

hmm.. when i try, numerator part and denominator part keep gets messed up :/

10. myininaya

$\frac{\cos(2x)}{1-\frac{\sin^4(x)}{\cos^4(x)}} \cdot \frac{\cos^4(x)}{\cos^4(x)}$ $\frac{\cos^4(x) \cos(2x)}{\cos^4(x)-\sin^4(x)}=\frac{\cos^4(x)\cos(2x)}{\cos(2x)}=\cos^4(x)$

11. myininaya

since we already showed $\cos^4(x)-\sin^4(x)=\cos(2x)$ earlier

12. anonymous

great! thanks a lot.

13. myininaya

you got it? :)

14. anonymous

yup i've tried it out myself! thanks for the help.