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)#