## anonymous one year ago prove this trigonometric equation; - tan^2x + sec^2x = 1

1. UsukiDoll

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

2. UsukiDoll

hmm that's one of the identities only rearranged...

3. UsukiDoll

there is a trig identity which is $\tan^2x+1 =\sec^2x$

4. anonymous

yes, that is correct (the first response you made)

5. UsukiDoll

@lxoser subtract $\tan^2x$ on both sides for $\tan^2x+1 =\sec^2x$

6. anonymous

1 = sec^2x - tan^2x ?

7. UsukiDoll

yeah.. now if we rearrange this $1=\sec^2x-\tan^2x$ to $1= -\tan^2x+\sec^2x$

8. AakashSudhakar

Hm, if I recall correctly, this identity can be derived from the following expression: $\sin^2x + \cos^2x = 1$It's actually quite simple. Simply divide the entire equation by [cos(x)]^2. Then simply each individual term!

9. UsukiDoll

I think there's already an identity which is $\tan^2x+1 =\sec^2x$ then just rearrange the terms.

10. UsukiDoll

oh I see where you're going on this... xD

11. AakashSudhakar

Oh, I wasn't sure whether or not he wanted that identity derived as well. Either way, rearranging the terms becomes simple once you know the direction to go in!

12. anonymous

im confused now :/

13. UsukiDoll

there are 3 trig identities.. two of them were posted here but I think using one of the identities would make it a bit easier

14. UsukiDoll

$$\color{blue}{\text{Originally Posted by}}$$ @UsukiDoll there is a trig identity which is $\tan^2x+1 =\sec^2x$ $$\color{blue}{\text{End of Quote}}$$

15. AakashSudhakar

@lxoser, do you know what the question exactly asks you? Does it simply ask to derive the expression you have from any trig identity, or does it want you to derive it from a specific identity? In any case, both my answer and @UsukiDoll's answers are correct, just using/manipulating different trig identities.

16. UsukiDoll

17. anonymous

the full question is ; verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation

18. UsukiDoll

it's one of those trig proofs... so start from the left to achieve the right the thing is that whatever was presented to us is similar to a trig identity, so we can use that particular trig identity, manipulate it a bit, and then we got the right side

19. AakashSudhakar

Unfortunately, I'm not quite sure what that means. Does it want both sides of the equation to be equal?

20. anonymous

okay so what i understand is - tan^2x + sec^2x = 1 is just the reverse of the trigonometric identity tan^2x + 1 = sec^2x & yes pretty much.

21. UsukiDoll

$-\tan^2x+\sec^2x=1$ using the identity $\tan^2x+1 =\sec^2x$ subtract $\tan^2x$ from both sides $1 =\sec^2x-tan^2x$ rearrange $1 =-tan^2x+sec^2x$

22. anonymous

23. UsukiDoll

if we substitute either way, it's equal like.. $1 =-\tan^2x+\sec^2x$ As in 1 is equal to that ^ then sub it to the original question -\tan^2x+\sec^2x= (-\tan^2x+\sec^2x) both equal similarly 1 =1

24. anonymous

okay, i see now.

25. UsukiDoll

ugh my latex broke

26. UsukiDoll

but we got them to equal.. that's the main thing

27. anonymous

i understand now, thank you sooo much!!