beautifulmymy123
  • beautifulmymy123
tan^2x + sec^2x = 1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Nerdsarecool
  • Nerdsarecool
What is the question
beautifulmymy123
  • beautifulmymy123
Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.
Nerdsarecool
  • Nerdsarecool
Give me a sec

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Nerdsarecool
  • Nerdsarecool
What kind of question is this
lfreeman1285
  • lfreeman1285
If you multiply everything by cos^2x then you'll have sin^2x + 1 = cos^2x, which is one of the other trig identities. I'm not sure if that helps or not.
Nerdsarecool
  • Nerdsarecool
You have so many people on it right now
beautifulmymy123
  • beautifulmymy123
I dont get this problem at all. Why would I multiply it by cos ^2x?
lfreeman1285
  • lfreeman1285
Are you trying to relate all of the trig identities to eachother?
beautifulmymy123
  • beautifulmymy123
yeah
lfreeman1285
  • lfreeman1285
The original one is sin^2x + cos^2x = 1. To get the other ones, you'd have to either divide by sin^2x or cos^2x. In the case of tan^2x - sec^2x = 1, sin^2x + cos^2x = 1 was divided by cos^2x. and then set equal to 1.
anonymous
  • anonymous
\[\sec ^2x-\tan ^2x=1\] adding \[2 \sec ^2x=2\] \[\frac{ 2 }{ \cos ^2x }=2\] \[2 \cos ^2x=2,1+\cos 2 x=2,\cos 2x=2-1=1=\cos 2 n \pi\] \[2x= 2 n \pi,x=n \pi, \] where n is an integer.
anonymous
  • anonymous
\[\tan ^2x+\sec ^2x=1\] it is not an identity. the problem can be solve it or find x.
beautifulmymy123
  • beautifulmymy123
wait I might be wrong, so would it be sin^2x+cos^2x all divided by cos^2x?
tkhunny
  • tkhunny
No, you're not wrong. The sign doesn't match up.
beautifulmymy123
  • beautifulmymy123
This is so confusing :/
tkhunny
  • tkhunny
Do it!! \(\sin^{2}(x) + \cos^{2}(x) = 1\) \(\dfrac{\sin^{2}(x)}{\cos^{2}(x)} + \dfrac{\cos^{2}(x)}{\cos^{2}(x)} = \dfrac{1}{\cos^{2}(x)}\) \(\tan^{2}(x) + 1 = \sec^{2}(x)\)
lfreeman1285
  • lfreeman1285
All of the trig functions are related by the unit circle (which has a radius of 1). the coordinates along the unit circle are similar to regular coordinates. The cosine value is equal to x. The sine value is equal to y. If you plug all those into the pythagorean theorem, then cos^2x + sin^2x = 1. From there, you either divide by sine or cosine to get the other trig identities. The original divided by sine is cot^2x + 1 = csc^2x The original divided by cosine is tan^2x +1 = sec^2x.
beautifulmymy123
  • beautifulmymy123
ok i think i understand that
lfreeman1285
  • lfreeman1285
Therefore, I don't think the identity tan^2x + sec^2x = 1 can be verified.
beautifulmymy123
  • beautifulmymy123
ok i think i understand that
lfreeman1285
  • lfreeman1285
Because its not one of the identities.
tkhunny
  • tkhunny
Really bad language. If it's an "Identity", it CAN be verified. If it cannot be verified, it is NOT an Identity.
tkhunny
  • tkhunny
It may be true for some values.
beautifulmymy123
  • beautifulmymy123
Thank you. That is why I was so confused.

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