limits annd derivatives

d(cosec xcot x)/dx = d(cosx/sin²x)/dx

   = {sin²x d(cosx)/dx - cosx d(sin²x)/dx}/sin⁴x

= {sin²x (-sinx) - cosx (2sinxcosx)}/sin⁴x

= -sinx{sin²x + 2cos²x}/sin⁴x

= -sinx{1 + cos²x}/sin⁴x

= -{1 + cos²x}/sin³x

= - cosec³x - cosecx cot²x

Regards,

Team,

TopperLearning.