Question

(tanx)p+(tany)q=tanz​

Answer 1

Answer:

      Ф[ sin(x) / sin(y) , sin(y) / sin(z) ] = 0

Step-by-step explanation:

We are going to see the general solution.

           dx/tan(x) = dy/tan(y) = dz/tan(z)

             cot(x)dx = cot(y)dy = cot(z)dz

This implies

               cot(x)dx = cot(y)dy

Taking integral on both sides we get

       log(sin(x)) = log(sin(y)) + log(c)         where log(c) is the constant

                     c = sin(x) / sin(y)

And

NOW

         cot(y)dy = cot(z)dz

Taking integral on both sides we get

       log(sin(y)) = log(sin(z)) + log(e)         where log(e) is the constant

                     e = sin(y) / sin(z)

Thus

                Ф[ sin(x) / sin(y) , sin(y) / sin(z) ] = 0