If Cotx+tanx=2cosecx find x

Question

Trigonometric question mathematics to find the value of x general solution .

Answer 1

 

cot(x)+tan(x)=2cosec(x)

cos(x)/sin(x)+sin(x)/cos(x)=2/sin(x)  (multiply by sin(x)cos(x))

cos²(x)+sin²(x)=2cos(x)

2cos(x)=1

cos(x)=1/2

x=±(π/3)+2πk, k Integer