How do you simplify $sin2theta -tan2theta$ using the double angle identities?

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Answer 1 · 2016-07-25T05:13:01

$sin2theta-tan2theta$

$=(2tantheta)/(1+tan^2theta)-(2tantheta)/(1-tan^2theta)$

$=(2tantheta(1-tan^2theta-1-tan^2theta))/((1+tan^2theta) (1-tan^2theta))$

$=(-2tantheta(2tan^2theta))/((1+tan^2theta)(1-tan^2theta))$

$=-(4tan^3theta)/((1+tan^2theta)(1-tan^2theta))$

$=(4tan^3theta)/(tan^4theta-1)$

How do you simplify sin2theta -tan2thetasin2theta -tan2theta using the double angle identities?