What is #csc(theta/2)# in terms of trigonometric functions of a unit #theta#?

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Answer 1 · 2016-05-23T10:22:14

#csc(theta/2)=sqrt(2/(1-costheta))#

Recall #cos2A=1-2sin^2A#

i.e. #2sin^2A=1-cos2A#

or #sin^2A=(1-cos2A)/2#

or #sinA=sqrt((1-cos2A)/2)#

Putting #2A=theta# or #A=theta/2#

Hence, #sin(theta/2)=sqrt((1-costheta)/2)#

or #csc(theta/2)=sqrt(2/(1-costheta))#