4. simplify the expression. (6 points) sine of x to the second power minus one divided by cosine of negative x a) -sin x b) cos x c) sin x d) -cos x 5. find all solutions in the interval [0, 2π). (6 points) sin2x + sin x = 0 a) x = 0, π, four pi divided by three , five pi divided by three b) x = 0, π, pi divided by three , two pi divided by three c) x = 0, π, pi divided by three , five pi divided by three d) x = 0, π, three pi divided by two

4. Simplify the expression.
sine of x to the second power minus one divided by cosine of negative x

(1−sin2(x))/(sin(x)−csc(x))

sin2x+cos2x=1 1−sin2x=cos2x

cos2(x)/(sin(x)−csc(x)) csc(x)=1/sin(x) cos2(x)/(sin(x)− 1/sin(x))= cos2(x)/((sin2(x)− 1)/sin(x)) sin2(x)− 1=-cos2(x) cos2(x)/(( -cos2(x))/sin(x))
=-sin(x)
the answer is the letter a) -sin x

5. Find all solutions in the interval [0, 2π). (6 points)
sin2x + sin x = 0
 using a graphical tool  
the solutions   x1=0 x2=pi x3=3pi/2
the answer is the letter D) x = 0, π, three pi divided by two

2(n-9) = 3(n + 5)
2n - 18 = 3n + 15
2n - 3n = 15 + 18
-n = 33
n = -33