How do you simplify $f(theta)=csc2theta-sec2theta-3cot2theta$ to trigonometric functions of a unit $theta$ ?

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Answer 1 · 2017-10-14T18:20:44

$f(theta)=1/(sin(2theta))=1/(2sinthetacostheta)-1/(2cos^2theta-1)-(2-1tan^2theta)/(2tantheta)$

Break the function down by term:
$csc(2theta)=1/(sin(2theta))=1/(2sinthetacostheta)$

$sec(2theta)=1/(cos(2theta))=1/(cos^2theta-sin^2theta)=1/(2cos^2theta-1)$

$cot(2theta)=1/tan(2theta)=(1-tan^2theta)/(2tantheta)$

Put this hell together:

$f(theta)=1/(sin(2theta))=1/(2sinthetacostheta)-1/(2cos^2theta-1)-(3-3tan^2theta)/(2tantheta)$

How do you simplify f(theta)=csc2theta-sec2theta-3cot2thetaf(theta)=csc2theta-sec2theta-3cot2theta to trigonometric functions of a unit thetatheta?