3tanx+cotx=5cosecx ,x is greater than 0 and less than 90. find value of x

3tanx+cotx=5cosecx

Multiply both sides with sinx* cosx

3(sinx)^2 + (cosx)^2 = 5cosx

We know (sinx)^2=1-(cosx)^2

3-3*(cosx)^2 + (cosx)^2=5cosx

let cosx=t
3-3t^2 + t^2=5t
0=2(t^2 )+5t-3
2(t^2 )+5t-3=0
(2t-1)(t+3)=0

so
2t-1=0 or t+3=0
so t=1/2 or t=-3
but t= cosx > -1, so t is not -3
Hence t=1/2
That is, cosx=1/2

Therefore x=60degrees