trigonometry question

Question

Find the solution set of each equation in the interval: 0 ≤ x < 2 : sin x + csc x – 2 = 0

a. {0}

b. {π/2, 3π/2}

c. {0,π}

d. π/2

Answer 1

sinx+cscx-2=0

csc=1/sin

substitute

sinx+(1/sinx)-2=0

multiply both sides by sinx

sin^2x+1-2sinx=0

sin^2x-2sinx+1=0

factor

(sinx-1)(sinx-1)=0

sinx-1=0

sinx=1

sin is equal to 1 at x=90° which is d.