Prove the identity Csc x sin x cot x cos x Note that each

Prove the identity. Csc x - sin x = cot x cos x Note that each Statement must be based on a Rule chosen from the Rule menu. To see a detailed description of a Rule, select the corresponding question mark.

Solution

cscx -sinx

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

=(1 -sin²x)_/sinx............................................cross multiply

=(cos²x)_/sinx............................................since sin²x+cos²x=1 is an identity

=(cosx*cosx)_/sinx

=(cosx_/sinx)*cosx

=cotx cosx......................................................since cosx_/sinx =cotx