## milliex51 3 years ago How do I prove (1-cos2x)(1+tan2x)=tan2x?

1. milliex51

do I solve it like this: $(\sin ^{2}x)(1+\tan ^{2x})$ $\sin ^{2x}\div1\times(sinx \div cosx)$ $\sin ^{2x}cosx \div sinx$

2. milliex51

x is suppose to be down, oops.

3. FoolForMath

Are you sure that is true: http://www.wolframalpha.com/input/?i=+%28%281-cos+2x%29%281%2Btan+2x%29%29+%3D%3D+tan+2x

4. experimentX
5. milliex51

false? .. oh.

6. milliex51

how would I know when it's false on a test?

7. experimentX

1# wolfram says so 2# it is giving solution ... this is only true in certain points. not on every ponits

8. milliex51

i don't understand..

9. experimentX
10. experimentX

sin(x) = cos(pi/2 - x) <---- put any value of x, you will always find it true!!

11. FoolForMath

I don't know how this TrueQ works: http://www.wolframalpha.com/input/?i=TrueQ%5Bsin+%5E2+x+%2B+cos+%5E2+x+%3D+1%5D

12. experimentX

LOL .. i found it a little while ago

13. TransendentialPI

Why not just expand the left side and do some cancelling?

14. milliex51

that's what I tried but then there's going to be no sinx at the bottom?

15. experimentX

It is equivalent to .. proving $$\-cos 2x ( 1 +\tan2x) - 1 = 0$$ $$\implies \cos2x + \sin2x + 1 = 0$$ <--- which is a false identity!!

16. experimentX

$$(\tan2x + 1) - (\tan2x+1)\cos2x = \tan 2x$$ $$\implies 1 - (\tan2x+1)\cos2x = 0$$