Question

How do you simplify `f(theta)=sin4theta-2tan2theta+5csc2theta` to trigonometric functions of a unit `theta`?

Answer 1

`f(theta)=2(2 sin theta*cos theta)(cos^2 theta-sin^2 theta)-(4 tan theta)/(1-tan^2 theta)+5/(2 sin theta cos theta)`

Explanation:

To simplify the equation to functions of unit `theta`

Use the following

`sin 2theta=2*sin theta cos theta`

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

`tan 2theta=(2*tan theta)/(1-tan^2 theta)`

`csc 2theta=1/(sin 2theta)=1/(2 sin theta cos theta)`

Start with the given

`f(theta)=sin 4theta-2*tan 2theta+ 5 csc 2theta`

`f(theta)=2*sin 2theta *cos 2theta-2((2*tan theta)/(1-tan^2 theta))+5(1/(2 sin theta cos theta))`

`f(theta)=2(2 sin theta*cos theta)(cos^2 theta-sin^2 theta)-(4 tan theta)/(1-tan^2 theta)+5/(2 sin theta cos theta)`

I hope this one helps . It is already expressed in unit `theta`.

Have a nice day ...from the Philippines!