we know that
The Cosecant is a trigonometric function that is the reciprocal of the sine
so

In this problem
Find the csc(B)

substitute the values

so

Find the csc(C)
substitute the values

Simplify

so

Statements
case A) csc right triangle B right triangle equals fraction
over

The statement is false
Because, the value of csc(B) equals fraction
over

case B) csc right triangle C right triangle equals fraction
over

The statement is true
See the procedure
case C) csc right triangle B right triangle equals fraction
over

The statement is true
See the procedure
case D) csc right triangle C right triangle equals fraction
over

The statement is false
Because, Because, the value of csc(C) equals fraction
over
