How do you simplify $cos2theta -tan2theta$ using the double angle identities?

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Answer 1 · 2017-01-02T07:14:17

$cos2theta-tan2theta=(1-tan^2theta)/(1+tan^2theta)-(2tantheta)/(1-tan^2theta)$

$cos2theta-tan2theta$ ,

now using $tan2theta=(2tantheta)/(1-tan^2theta)$ and $cos2theta=(cos^2theta-sin^2theta)$ , the above is equal to

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

Note that we have used $cos^2theta-sin^2theta=1$

The above can be further simplified as

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

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

How do you simplify cos2theta -tan2thetacos2theta -tan2theta using the double angle identities?