## anonymous one year ago Prove - tan^2(x) + sec^2(x) = 1 by working on one side to match the other using identities.

1. anonymous

$- \tan^2x + \sec^2x = 1$

2. anonymous

$- \tan^2x + \sec^2x = 1$

3. Nnesha

sec^2 theta = what ? remember the identity ?

4. anonymous

1/cos^2x

5. Nnesha

well that's reciprocal of sec but it's okay we can use that too!! tan^2 =what ?

6. anonymous

sin^2x/cos^2x

7. anonymous

or 1/cot^2x

8. Nnesha

yes right so replace tan and sec with that $\huge\rm -\frac{ \sin^2x }{ \cos^2x } +\frac{ 1 }{ \cos^2x}$ find the common denominator

9. anonymous

cos^2x?

10. Nnesha

ohh well not gonna work should use the identity i guess

11. anonymous

You could also use the fact that $$\sf sec^2(\theta) = tan^2(\theta) +1$$ and then substitute this in place of $$\sf \sec^2(\theta)$$

12. anonymous

thats true, thanks

13. anonymous

$\sf -tan^2(\theta)+\sec^2(\theta) = 1$$\sf -\tan^2(\theta) +\color{red}{\tan^2(\theta) +1}=1$

14. anonymous

Wow... The one identity I didn't think of solved it so easily. Thank you!

15. Nnesha

$\huge\rm \frac{ -\sin^2x +1}{ \cos^2 }$ use the special identity sin^2x+cos^2x =1 solve for cos^2

16. anonymous

No problem :)

17. Nnesha

here you can copy these identities http://www.math.com/tables/trig/identities.htm you weren't familiar with this so that's why i thought better to write interms of sin and cos

18. anonymous

That's a good way to approach it too. @Nnesha :)

19. anonymous

Thanks that will help too @Nnesha

20. Nnesha

yw :=)