Question

How do you simplify `f(theta)=2csc2theta-cos2theta+sec2theta` to trigonometric functions of a unit `theta`?

Answer 1

f(t) = 2csc 2t - 2cos 2t + sec 2t
`A = 2/(sin 2t) = 2/2sin tcos t = 1/(sin tcos t)`
`B = - cos 2t = -(1 - 2sin^2 t) = 1 - 2sin^2 t =`
`= (1 - sqrt2sint)(1 + sqrt2sin t)`
`C = 1/(cos 2t) = 1/(1 - 2sin^2 t) = 1/((1 - sqrt2sin t)(1 + sqrt2sin t))`
Finally,
f(t) = A + B + C
`f(t) = 1/(sin t.cos t) + (1 - sqrt2sint)(1 + sqrt2.sin t) + 1/((1 + sqrt2sint)(1 - sqrt2sin t))`