Answer:
B. sin(theta) cos^2(theta)
Step-by-step explanation:
sin^2(theta) / csctheta tan^2(theta)
To solve, we convert to sine and cosine and then simplify.
means by the priority of operators (* and / from left to right)
(sin^2(theta) / csctheta) * tan^2(theta)
= sin^2(theta) / (1/sin(theta) * (sin(theta)/cos(theta)^2
= sin^2(theta) * sin(theta) * sin^2(theta) / cos^2(theta)
= sin^5(theta) / cos^2(theta)
which obviously does not correspond to any of the answers.
IF the expression were missing parentheses in the denominator, then it becomes:
sin^2(theta) / (csctheta tan^2(theta))
= sin^2(theta) / (1/sin(theta) * sin^2(theta) /cos^2(theta))
= sin^2(theta) / (sin(theta)/cos^2(theta)
= sin(theta) cos^2(theta)
which corresponds to answer B.
