cscx/cotx+tanx=cosx

Question

how do i establish identity

Answer 1

cscx/(cotx+tanx) = cscx/(1/tanx + tanx)

 

                        = cscx/[(1+tan²x)/tanx]   

 

                        = cscx/[sec²x/tanx]

 

                        = (cscx)(tanx)/sec²x

 

                        = (cscx)(tanx)(cos²x)

 

                        = (1/sinx)(sinx/cosx)(cos²x) = cosx

 

 

Answer 2

csc / cot + tan = cos

(1/sin)(sin/cos) + sin / cos = cos

1/cos + sin / cos = cos

 

Something needs to be changes?