Question

If `y=1/2log((1-cos2x)/(1+cos2x)),p rov et h a t(dy)/(dx)=2cos e c2x`

Answer 1

`y=1/2log((1-cos2x)/(1+cos2x))`
`1-cos2x=2sin^2x`
`1+cos2x=2cos^2x`
`y=1/2log(2sin^2x)/(2cos^2x)`
`=1/2log tan^2x`
`y=logtanx`
`dy/dx=1/(tanx)xxsec^2x`
`=(1/cos^2x)/(sinx/cosx)`
`=2/sin^2x`
`=2cosec2x`