Question

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

Answer 1

`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)`