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y = log(sqrt((1-cos(3x/2))/(1+ cos(3x/2)...

y = `log(sqrt((1-cos(3x/2))/(1+ cos(3x/2))))` differentiate w.r.t. x.

Text Solution

Verified by Experts

`y=logsqrt((1-cos3x/2)/(1+cos3x/2))`
`y=logsqrt((2sin^23/4x)/(2cos^23/4x)`
`y=logsqrt(tan^23/4x)`
`y=log(tan3/4x)`
`dy/dx=1/(tan3/4x)sec^2(3/4x)*3/4`
`dy/dx=3/4(sec^2 3/4x)/(tan3/4x)`
`dy/dx=3/4(1/cos^2 3/4x)/((sin3/4x)/(cos3/4x))`
`dy/dx=3/4*sec3/4xcosec3/4x`
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