Can anyone help me verify the identity?

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Answer 1 · 2017-11-08T08:33:00

See below.

#(cosucotu)/(1-sinu)-1=cscu#

LHS #= (cosu*cosu/sinu)/(1-sinu)-1#

#= cos^2u/((1-sinu)*sinu)-1#

#= (cos^2u-(sinu-sin^2u))/((1-sinu)*sinu)#

#= (sin^2u+cos^2u-sinu)/((1-sinu)*sinu)#

#= (1-sinu)/((1-sinu)*sinu)# [Since: #sin^2u+cos^2u=1#}

#= cancel(1-sinu)/(cancel(1-sinu)*sinu)#

#= 1/sinu = cscu#

#= #RHS