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

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Answer 1 · 2016-04-13T10:56:19

Please see below.

#(cscx-1)/(1-sinx)#

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

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

= #((1-sinx))/sinx xx1/((1-sinx))#

= #(cancel(1-sinx))/sinx xx1/(cancel(1-sinx))#

= #1/sinx#

= #cscx#