How do you verify #(cosxcotx)/(1-sinx)-1=cscx#?

1 Answer
P dilip_k
Mar 12, 2018

#LHS=(cosxcotx)/(1-sinx)-1#

#=(cosxcosx)/(sinx(1-sinx))-1#

#=(cos^2x)/(sinx(1-sinx))-1#

#=(1-sin^2x)/(sinx(1-sinx))-1#

#=((1-sinx)(1+sinx))/(sinx(1-sinx))-1#

#=(1+sinx)/sinx-1#

#=1/sinx+sinx/sinx-1#

#=cscx+1-1#

#=cscx=RHS#

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