Use the fundamental identities to fully simplify the expression.

cot(x)cos(x) + csc(x)sin^2(x)

I keep ending up with cos(x) + sin^2(x) or cos(x) + sin(x)...

csc(x)

Step-by-step explanation:

cotx cosx = cos^2x/sinx

cscx sin^2x = sinx

so, you have

cos^2x/sinx + sinx = (cos^2x + sin^2x)/sinx = 1/sinx = cscx

the equation of the parabola is y2=12x

explanation:

the vertex is midway between the focus ad the directrix

so, the vertex is (0,0)

let p=(x,y) be a point on the parabola.

the distance of p from the directrix is equal to the distance from the focus.

x+3=√(x−3)2+(y−0)2

(x+3)2=(x−3)2+y2

x2+6x+9=x2−6x+9+y2

y2=12x

graph{y^2=12x [-10, 10, -5, 5]}