Prove the identity csc x cot x cos x sin x Solution statem

Prove the identity csc x - cot x cos x = sin x

Solution

statement...........................................................................................................rule

cscx -cotxcosx

=(1_/sinx)-cotxcosx...........................................................................................cscx =1_/sinx

=(1_/sinx)-(cosx_/sinx)cosx..................................................................................cotx =cosx_/sinx

=(1-cos²x)_/sinx.................................................................................................sinx is common denominator

=(sin²x)_/sinx.......................................................................................................sin²x+cos²x=1

=sinx

therefore cscx -cotxcosx= sinx