What is the solution for cos tan csc equals 1?

Well I don't exactly get "the solution", but simplifying the equation is quite simple. Maybe that's what you're looking for. Here are the steps for simplifying it.

costancsc = 1

1. Change tan to sin/cos

2. Change csc to 1/sin

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

And as you can now see, the first cos cancels with the second one under the sin/cos fraction, and the first sin cancels with the second one under the 1/sin fraction consequentially leaving you with 1 = 1.

For a better look, notice this fraction when all three parts are combined

cos * sin * 1

----------------

cos * sin

See how the cos and sin cancel each other leaving you with 1 * 1 * 1 which is just 1. Therefore the final simplification is just 1 = 1.

I hope this helps!