Solve the equation I answered cotx 1 if this is not the an

Solve the equation

I answered: cotx - 1 , if this is not the answer (or is) please show steps/work to find the correct answer

Solution

csc(x)(sin²(x) + cos²(x)tan(x))/(sin(x) + cos(x)) = (1/sin(x))(sin²(x) + cos²(x)sin(x)/cos(x))/(sin(x) + cos(x))

= (sin(x) + cos(x))/(sin(x) + cos(x))   

= 1