Answer: sec^2(x)
Explanation:
This requires a fundamental understanding of trig expressions and relationships.
sin/cos is equivalent to the expression tan(x). With that being understood, sin^2(x)/cos^2(x) is equivalent to tan^2(x).
The next term in the equation is sin(x) * csc(x).
- csc(x) = 1/sin(x)
Therefore, this term is essentially sin(x) * 1/(sin(x)) which is equal to sin(x)/sin(x) or 1.
Now, we have the expression:
tan^2(x) + 1
This is a tricky problem because if you don't know your trig identities well, you may get stumped at this point. In this scenario, tan^2(x) + 1 = sec^2(x). You just have to memorize this identity.