Question

For csc^2 A-1/cot A csc A, what is the simplest equivalent trig expression? The answers I have to choose from are sin A, cosA, tan A or csc A, but I don't know how?? csc theta= 1/sin theta but its ^2. Help please I don't even no where to begin

Answer 1

csc=1/sin
cot=cos/sin
so,
csc^2-1/cotcsc =
((1/sin^2)-1)sin/(cos/sin) =
sin((sin/sin^2)-sin)/(cos) =
(sin^2/sin^2-sin^2)/cos =
(1-sin^2)/cos =
cos^2/cos = cos A

((sin^2/sin^2)-sin/(sin^2 cos)