How do you verify the identity #sintheta/(1-costheta)+(1-costheta)/sintheta=2csctheta#?

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Answer 1 · 2016-08-15T16:34:37

#LHS=sintheta/(1-costheta)+(1-costheta)/sintheta#

#=(sintheta*sintheta)/((1-costheta)sintheta)+(1-costheta)/sintheta#

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

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

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

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

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

#=2/sintheta=2csctheta=RHS#

Verified