Find all values of x in the interval [0, 2π] that satisfy the equation. (enter your answers as a comma-separated list.) 6 sin(2x) = 6 cos(x)

6 sin 2x = 6 cos x Using the identity sin 2x = 2 sin x cos x:-

12 sin x cos x = 6 cos x

6 cos x ( 2 sin x - 1) = 0

either 6 cos x = 0 or 2 sin x - 1 = 0 so sin x = 1/2

x = pi/2, 3pi/2 , pi/6, 5pi / 6

answer is ( pi/6, pi/2, 5pi/6, 2pi/2)

2 equivalent expressions to represent the area of a rectangle and the top is n-3 and the side is 2

area of the rectangle = length * width

given length = n - 3

width = 2

replace it in the area

so area of the rectangle = (n-3) *2

= 2(n-3)

one of the expression is 2(n-3)

to get another expression we distribute 2 inside the parenthesis

2(n-3) is 2n - 6

so another expression is 2n - 6

two equivalent expression are

2(n - 3)   , 2n - 6