How do you simplify #f(theta)=cot2theta-sin2theta+3tan2theta# to trigonometric functions of a unit #theta#?

1 Answer
Feb 25, 2016

#(1-tan^2theta)/(2tantheta) - 2sinthetacostheta + (6tantheta)/(1-tan^2theta)#

Explanation:

Using the following #color(blue)" Double angle identities "#

#• sin2theta = 2sinthetacostheta#

#• tan2theta = (2tantheta)/(1 - tan^2theta #

#• cot2theta = 1/(tan2theta) = (1 - tan^2theta)/(2tantheta) #

Replace these into appropriate terms to obtain

#(1-tan^2theta)/(2tantheta) - 2sinthetacostheta +(3(2tantheta))/(1-tan^2theta)#