anonymous
  • anonymous
-tan^2x + sec^2x=1
Mathematics
katieb
  • katieb
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mathstudent55
  • mathstudent55
Do you need to prove this identity?
anonymous
  • anonymous
Yes
mathstudent55
  • mathstudent55
Rewrite tan x and sec x in terms of sin x and cos x. Then multiply both sides by \(\cos^2 x\)

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anonymous
  • anonymous
Sec^2x=1/cos^2x
mathstudent55
  • mathstudent55
yes. what about tan? what is tan in terms of sin and cos?
anonymous
  • anonymous
I'm not sure😓
anonymous
  • anonymous
NO
anonymous
  • anonymous
U GAYY
triciaal
  • triciaal
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triciaal
  • triciaal
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mathstudent55
  • mathstudent55
Right. tan x = sin x / cos x
mathstudent55
  • mathstudent55
\(-\tan^2x + \sec^2x=1\) \(-\dfrac{\sin^2x}{\cos^2 x} + \dfrac{1}{\cos^2x}=1\) Now multiply both sides by \(\cos^2 x\)
anonymous
  • anonymous
ok :)
anonymous
  • anonymous
-sin^2x/cos^2x=cos^2x?
mathstudent55
  • mathstudent55
No
mathstudent55
  • mathstudent55
\(-\dfrac{\sin^2x}{\cos^2 x} + \dfrac{1}{\cos^2x}=1\) Now we multiply both sides by \(\cos ^2 x\) \( \cos^2 x(-\dfrac{\sin^2x}{\cos^2 x} + \dfrac{1}{\cos^2x})=1 \times \cos^2 x\) \( -\dfrac{\sin^2x \cancel{\cos^2 x}}{\cancel{\cos^2 x}~~1} + \dfrac{\cancel{\cos^2 x}~~1}{\cancel{\cos^2x}~~1})= \cos^2 x\) \(- \sin^2 x + 1 = \cos^2 x\) \(1 = \sin^2 x + \cos^2 x\) \(\sin^2 x + \cos^2 x = 1\) The last equation is a well-known trig identity.
anonymous
  • anonymous
thank you >.< ill work harder to memorize the identities

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