cot x = √2.
sin x cot x csc x = √2
convert to sin x and cos x:
sin x * cos x / sinx * 1/ sin x = √2
cos x / sin x = √2
cot x = √2 (answer).
first, find the intersections of the parabolas using any method. i choose to use the elimination method
next, find the distance between the intersected points (3, -1) & (-1, 2):
the sine is the ratio of the opposite side to the hypotenuse. when the ange is acute (< 90°), the hypotenuse is longer than the opposite side of the right triangle, so the ratio of that side length to the hypotenuse must be less than 1.