How do you simplify #f(theta)=-2csc(theta/4)-cot(theta/2)+2sin(theta/4)# to trigonometric functions of a unit #theta#?

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Answer 1 · 2016-07-23T00:32:51

#=(-2(1+sqrt(1/2(1+costheta))))/sqrt(1/2(1-sqrt(1/2(1+costheta))))-(1+costheta)/sintheta#

#f(theta)=-2csc(theta/4)-cot(theta/2)+2sin(theta/4)#

#=2sin(theta/4)-2/sin(theta/4)-cot(theta/2)#

#=(2sin^2(theta/4)-2)/sin(theta/4)-(2cos^2(theta/2))/(2sin(theta/2)cos(theta/2))#

#=(-2(1-sin^2(theta/4)))/sin(theta/4)-(1+costheta)/sintheta#

#=(-2cos^2(theta/4))/sin(theta/4)-(1+costheta)/sintheta#

#=(-2(1+cos(theta/2)))/sqrt(1/2(1-cos(theta/2)))-(1+costheta)/sintheta#

#=(-2(1+sqrt(1/2(1+costheta))))/sqrt(1/2(1-cos(theta/2)))-(1+costheta)/sintheta#

#=(-2(1+sqrt(1/2(1+costheta))))/sqrt(1/2(1-sqrt(1/2(1+costheta))))-(1+costheta)/sintheta#