How do you find the solutions of tanx equals 2cscx?

tanx=2cscx

sinx/cosx=2/sinx

sin2x/cosx=2

sin2x=2cosx

1-cos2x=2cosx

0=cos2x+2cosx-1

Quadratic formula:

cosx=(-2±√(2^2+4))/2

cosx=(-2±√8)/2

cosx=(-2±2√2)/2

cosx=-1±√2

cosx=approximately -2.41 or approximately 0.41.

Since the range of the cosine function is [-1,1], only approx. 0.41 works.

So:

cosx= approx. 0.41

Need calculator now (I went as far as I could without one!)

x=approx 1.148