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

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UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2\[\tan^2x+\sec^2x=1\] this?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2hmm that's one of the identities only rearranged...

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2there is a trig identity which is \[\tan^2x+1 =\sec^2x \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes, that is correct (the first response you made)

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2@lxoser subtract \[\tan^2x \] on both sides for \[\tan^2x+1 =\sec^2x \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.01 = sec^2x  tan^2x ?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2yeah.. now if we rearrange this \[1=\sec^2x\tan^2x \] to \[1= \tan^2x+\sec^2x\]

AakashSudhakar
 one year ago
Best ResponseYou've already chosen the best response.2Hm, 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!

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2I think there's already an identity which is \[\tan^2x+1 =\sec^2x \] then just rearrange the terms.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2oh I see where you're going on this... xD

AakashSudhakar
 one year ago
Best ResponseYou've already chosen the best response.2Oh, 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!

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2there are 3 trig identities.. two of them were posted here but I think using one of the identities would make it a bit easier

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2\(\color{blue}{\text{Originally Posted by}}\) @UsukiDoll there is a trig identity which is \[\tan^2x+1 =\sec^2x \] \(\color{blue}{\text{End of Quote}}\)

AakashSudhakar
 one year ago
Best ResponseYou've already chosen the best response.2@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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the 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

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2it'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

AakashSudhakar
 one year ago
Best ResponseYou've already chosen the best response.2Unfortunately, I'm not quite sure what that means. Does it want both sides of the equation to be equal?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay 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.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2\[\tan^2x+\sec^2x=1 \] using the identity \[\tan^2x+1 =\sec^2x \] subtract \[\tan^2x \] from both sides \[1 =\sec^2xtan^2x \] rearrange \[1 =tan^2x+sec^2x \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is that the final answer?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2if 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

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2but we got them to equal.. that's the main thing

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i understand now, thank you sooo much!!
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