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cotθ-tanθ/sinθcosθ=cscēθ-secēθ
Start with left-hand side
cotθ-tanθ/sinθcosθ
=((cos/sin)-(sin/cos))/sincos
=((cos^2-sin^2)/sincos)/sincos
=(cos^2-sin^2)/(sincos)^2
=(cos^2/sin^2cos^2)-(sin^2/sin^2cos^2)
=(1/sin^2)-(1/cos^2) =csc^2-sec^2
left-hand side = right-hand side
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