Find all the solution in the interval 02pi 2sinxcscx1 Find a

Solution

2sinx - cscx = 1 interval [0, 2pi)

2sinx - 1/sinx =1

2sin^2x - sinx -1 =0

2sin^2x +2sinx -sinx -1 =0

(2sinx-1)(sinx +1)=0

sinx = 1/2 ; x = pi/6 , 5pi/6

sinx = -1 ; x = pi

Solution : x = pi/6 , 5pi/6 , pi