Trigonometric equation

Question

1) cos(2x)=sin(x)

2) study continuity of this function:

sqrt(2/3-x)^2 if x>2/3

(2-3x)/(x-1) if x equal or < 2/3

Answer 1

1) Use double angle formula

cos 2x = sin x

1 - 2sin² x = sin x

0 = 2sin² x + sin x - 1

Can you solve for x and answer?"

2) What do you mean by ":study continuity?"