Question

How do you simplify `f(theta)=cot2theta-sin2theta+3tan2theta` to trigonometric functions of a unit `theta`?

Answer 1

`(1-tan^2theta)/(2tantheta) - 2sinthetacostheta + (6tantheta)/(1-tan^2theta)`

Explanation:

Using the following `color(blue)" Double angle identities "`

`• sin2theta = 2sinthetacostheta`

`• tan2theta = (2tantheta)/(1 - tan^2theta`

`• cot2theta = 1/(tan2theta) = (1 - tan^2theta)/(2tantheta)`

Replace these into appropriate terms to obtain

`(1-tan^2theta)/(2tantheta) - 2sinthetacostheta +(3(2tantheta))/(1-tan^2theta)`