The expression oos² θ/sin θ + sin θ is equivalent to
1) 1 + cos² θ
2) cos² θ
3) sin θ
4) csc θ
(1-sin^2)/sin + sin
1/sin - sin + sin
1/sin
= csc
To simplify the expression oos² θ/sin θ + sin θ, we can start by simplifying the denominator of the first fraction, which is sin θ.
The expression becomes: (cos² θ)/sin θ + sin θ
Next, let's find a common denominator for the two fractions. The common denominator will be sin θ.
The expression now becomes: (cos² θ)/sin θ + sin² θ/sin θ
To add these two fractions, we need a common denominator, which is sin θ.
The expression now becomes: (cos² θ + sin² θ)/sin θ
Using the Pythagorean identity cos² θ + sin² θ = 1, we can simplify the expression further.
The expression becomes: 1/sin θ
Recall the reciprocal trigonometric identity csc θ = 1/sin θ.
Therefore, the expression oos² θ/sin θ + sin θ is equivalent to option 4) csc θ.