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

1 Answer
Oct 14, 2017

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

Explanation:

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)#