How do you simplify $f(theta)=csc4theta-2cot2theta+5sec2theta$ to trigonometric functions of a unit $theta$ ?

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Answer 1 · 2016-11-21T09:23:18

$f(theta)=csc4theta-2cot2theta+5sec2theta$

$=1/(sin4theta)-(2cos2theta)/(sin2theta)+5/(cos2theta)$

$=1/(2sin2thetacos2theta)-(2cos2theta)/(sin2theta)+5/(cos2theta)$

$=(1-4cos^2 2theta+10sin2theta)/(2sin2thetacos2theta)$

$=(1-4(2cos^2 theta-1)^2+20sinthetacostheta)/(4sinthetacostheta(2cos^2theta-1))$

How do you simplify f(theta)=csc4theta-2cot2theta+5sec2thetaf(theta)=csc4theta-2cot2theta+5sec2theta to trigonometric functions of a unit thetatheta?