How do you prove #(Cot(x) - tan(x)) /( sin(x) cos(x)) = csc^2(x) - sec^2(x)#?

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Answer 1 · 2016-05-05T20:46:15

see below

Left Side:#=(cosx/sinx -sinx/cosx)/(sinxcosx)#

#=((cos^2x-sin^2x)/(sinxcosx))/(sinxcosx)#

#=(cos^2x-sin^2x)/(sinxcosx) xx 1/(sinxcosx)#

#=(cos^2x-sin^2x)/(sin^2xcos^2x)#

#=cos^2x/(sin^2xcos^2x) - sin^2x/(sin^2xcos^2x)#

#=1/sin^2x - 1/cos^2x#

#=csc^2x-sec^2x#

#=# Right Side