haleyking345
tan^2x - tan^2x sin^2x = sin^2x
How in the world could you solve this?
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TuringTest
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\[\tan^2x-\tan^2x\sin^2x=\tan^2x(1-\sin^2x)\]and what is the identity for \(1-\sin^2x\) ?
haleyking345
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cos^2x
TuringTest
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right, so now what do you have on the left?
haleyking345
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tan^2x-tan^2xsin^2x=tan^2x
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no, I mean after what we just did...
haleyking345
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tan^2x
TuringTest
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\[\tan^2x-\tan^2x\sin^2x=\tan^2x(1-\sin^2x)=\tan^2x\cos^2x=?\]
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use\[\tan x=\frac{\sin x}{\cos x}\]
haleyking345
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that would leave you with sin^2x as the answer
TuringTest
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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.