tanx(1-sin^2x)=1/2sin2x

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[1-\sin^2(x)=\cos^2(x)\] Plug in, multiply by sin(x)/cos(x) (ends up being sin(x)cos(x)) and simplify.
I got that part. and tanx becomes sinx/cosx, which leaves me with sinx/cosx(cos^2x) whats after that? algebra?
i end up with sinx/cosx but how does that equal 1/2sin2x?

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Other answers:

Is it (1/2)sin2x or 1/(2sin(2x)?
(1/2)sin2x
Okay, sin(x)/sin(2x) simplifies to 1/(2cos(x)).\[\sin(x)\cos(x) = (1/2)\sin(2x) \rightarrow\] Seems like if we go down this road, we're just going to end up with 1/2 = 1/2...
whatt identity would that be?
sin(2x) = 2sin(x)cos(x)

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