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taylonrlongmore
taylonrlongmore taylonrlongmore
  • 27-02-2017
  • Mathematics
Answered

sin2x/1+cos2x=tanx

How do I prove this with the double angle law

Verified Answer :

wizard123
wizard123 wizard123
  • 27-02-2017

\(sin(2x) = 2 sin x cos x \\ \\ cos(2x) = cos^2 x - sin^2 x\)
After Substituting:
\(\frac{2 sin x cos x}{1+cos^2 x - sin^2 x}\)
Use pythagorean thm:
\(1 - sin^2 x = cos^2 x\)
......................
\(\frac{2 sin x cos x}{2cos^2 x} \\ \\ = \frac{sinx }{cos x} \\ \\ = tan x\)

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