Find all solutions of the equation in the interval 0 2pi Ent

Find all solutions of the equation in the interval (0, 2pi). (Enter your answers as a comma-separated list. If the 4 sin^2 x + 6 sin x + 2 = 0 Use inverse functions where needed to find all solutions of the equation in the interval [0, 2pi). (Enter your answers cot^2 x - 5 cot x + 4 = 0

Solution

5)4sin²x+6sinx +2=0

4sin²x+4sinx+2sinx +2=0

4sinx(sinx +1)+2(sinx +1)=0

(sinx +1)(4sinx +2)=0

sinx =-1, sinx =-2/4

sinx=-1, sinx =-1/2

x=3pi/2 ,7pi/6,11pi/6

6)cot²x-5cotx +4=0

cot²x-cotx-4cotx +4=0

cotx(cotx -1)-4(cotx -1)=0

(cotx -4)(cotx -1)=0

cotx =4 ,cotx =1

x=cot^-1(4) ,pi/4 ,5pi/4