Question

Question #f236b

Answer 1

`cos2x`

Explanation:

Use the following identities to solve the problem

•`tantheta = sintheta/costheta`

•`cos^2theta + sin^2theta = 1`

•`cos2theta = cos^2theta - sin^2theta`

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`=(1 - sin^2x/cos^2x)/(1 + sin^2x/cos^2x)`

`= ((cos^2x - sin^2x)/cos^2x)/((cos^2x+ sin^2x)/cos^2x)`

`= (cos^2x- sin^2x)/cos^2x * cos^2x/(cos^2x + sin^2x)`

`= cos^2x - sin^2x`

`= cos2x`

Hopefully this helps!