Find the derivative of #ln(sqrt(((1-cosx))/((1+cosx))))#?

Question

5474 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-08T15:05:37

#d/(dx)ln(sqrt(((1-cosx))/((1+cosx))))=cscx#

#ln(sqrt(((1-cosx))/((1+cosx))))#

= #ln(sqrt((2sin^2(x/2))/(2cos^2(x/2))))#

= #ln(tan(x/2))#

Hence #d/(dx)ln(sqrt(((1-cosx))/((1+cosx))))#

= #d/(dx)ln(tan(x/2))#

= #1/tan(x/2)xxsec^2(x/2)xx1/2#

= #cos(x/2)/sin(x/2)xx1/cos^2(x/2)xx1/2#

= #1/(2sin(x/2)cos(x/2)#

= #1/sinx#

= #cscx#