anonymous
  • anonymous
tan^2x - tan^2x sin^2x = sin^2x How in the world could you solve this?
Mathematics
katieb
  • katieb
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TuringTest
  • TuringTest
\[\tan^2x-\tan^2x\sin^2x=\tan^2x(1-\sin^2x)\]and what is the identity for \(1-\sin^2x\) ?
anonymous
  • anonymous
cos^2x
TuringTest
  • TuringTest
right, so now what do you have on the left?

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anonymous
  • anonymous
tan^2x-tan^2xsin^2x=tan^2x
TuringTest
  • TuringTest
no, I mean after what we just did...
anonymous
  • anonymous
tan^2x
TuringTest
  • TuringTest
\[\tan^2x-\tan^2x\sin^2x=\tan^2x(1-\sin^2x)=\tan^2x\cos^2x=?\]
TuringTest
  • TuringTest
use\[\tan x=\frac{\sin x}{\cos x}\]
anonymous
  • anonymous
that would leave you with sin^2x as the answer
TuringTest
  • TuringTest
which is what you have on the left, which proves the identity if you want a solution, the answer is \(\mathbb R\), but I think the point here was just to prove the identity.

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