Question

How do you simplify `f(theta)=csc2theta-sin2theta-5sec2theta` to trigonometric functions of a unit `theta`?

Answer 1

`f(theta) = 1/{2 sin theta cos theta} -2 sin theta cos theta - 5/{2 cos ^2 theta -1 }`

Explanation:

Here are the double angle formulas:

`cos(2 theta) = 2 cos^2 theta - 1 quad` among others

`sin(2 theta) = 2 sin theta cos theta`

`f(theta) = csc(2 theta) - sin(2 theta) - 5 sec(2 theta)`

`f(theta) = 1/sin(2 theta) - sin (2 theta) -5/cos(2theta)`

`f(theta) = 1/{2 sin theta cos theta} -2 sin theta cos theta - 5/{2 cos ^2 theta -1 }`