Question

How do you simplify `f(theta)=2tan2theta-cos2theta+sec2theta` to trigonometric functions of a unit `theta`?

Answer 1

`2tan2theta-cos2theta+sec2theta={1+4sinthetacostheta}/(2cos^2theta-1)-(2cos^2theta-1)`

Explanation:

`f(theta)=2tan2theta-cos2theta+sec2theta`

= `2(sin2theta)/(cos2theta)-(2cos^2theta-1)+1/(cos2theta)`

= `{1+2(2sinthetacostheta)}/(2cos^2theta-1)-(2cos^2theta-1)`

= `{1+4sinthetacostheta}/(2cos^2theta-1)-(2cos^2theta-1)`