Find the derivative of d{(tanx-cosx)/sinx.cosx}/dx

Steps to solve Find the derivative of d{(tanx-cosx)/sinx.cosx}/dx

=(tanx-cosx)/sinx.cosx

={(sinx/cosx)-cosx}/sinx.cosx

={(sinx/sinx.cos^2x)-(cos^2x/sinx.cos^2x)}

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

=(sec^2x-cosecx)

Hence the derivative is 

=d(sec^2x-cosecx)/dx

=d(sec^2x)/dx-d(cosecx)/dx

=2secx(secx+tanx)+cosecx.cotx

=2sec^2x.tanx+cosecx.cotx

Hence the derivative of d{(tanx-cosx)/sinx.cosx}/dx is 2sec^2x.tanx+cosecx.cotx

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