Answer:
csc
A
, as desired!
Step-by-step explanation:
cos
2
A
sin
A
+
sin
2
A
cos
A
,
=
cos
2
A
cos
A
+
sin
2
A
sin
A
sin
A
cos
A
,
=
cos
(
2
A
−
A
)
sin
A
cos
A
,
=
cos
A
sin
A
cos
A
,
=
1
sin
A
,
=
csc
A
, as desired!
I believe that A and D would be the correct answer. Because both are 30,60,90 triangles and would be congruent. The other 2 triangles only have 1 angle and their side measures are at two different places meaning they cannot be congruent.

check your calculator for the [!] factorial button.
also bear in mind that most calculators also have an [ₙPᵣ] button, to get Permuations, and you can just use that.
1/2, because 9/16 is closer to 8/16 which reduces to 1/2. It is not as close to 0/16 (0) or 16/16 (1)