Question

How do you simplify `f(theta)=2tan2theta-3sin2theta+csc2theta` to trigonometric functions of a unit `theta`?

Answer 1

`2tan 2t = (4tan t)/(1 - tan^2 t)`
`3sin 2t = 6sin t.cos t`
`csc 2t = 1/sin (2t) = 1/(2sin t.cos t)`
Finally,
`f(t) = (4tan t)/(1 - tan^2 t) - 6sin t.cos t + 1/(2sin t.cos t)`