Please solve this question for me with step by step solution

write it as 3^(tan^2x)*sqrt((3y –  1)^2 + 1)

now tan^2x is greater than or equal to zero 

so  3^(tan^2x) is greater than or equal to 1.

also (3y –  1)^2 is greater than or equal to zero 

or (3y –  1)^2 + 1 is greater than or equal to 1

or sqrt((3y –  1)^2 + 1) is greater than or equal to 1

hence the product 3^(tan^2x)*sqrt((3y –  1)^2 + 1) is greater than or equal to 1. so for the inequality to hold, it can only hold if 3^(tan^2x)*sqrt((3y –  1)^2 + 1) is equal to 1.

which happens when tan^2x=0 or x=0, pi, 2pi, 3pi

and (3y –  1)^2 + 1) =1

or y= 1/3

so the number of solutions is 4.

kindly approve :)