Answer:
Answer: choice D.
Step-by-step explanation:
Trigonometric Functions
We need to recall some properties and definitions of the trigonometric functions.
[tex]\displaystyle \tan \theta=\frac{\sin\theta}{\cos\theta}[/tex]
[tex]\displaystyle \sec \theta=\frac{1}{\cos\theta}[/tex]
We need to simplify the following expression:
[tex]5\sin\theta\sec\theta[/tex]
Substituting the identity for the secant:
[tex]\displaystyle 5\sin\theta\sec\theta=5\sin\theta.\frac{1}{\cos\theta}[/tex]
Operating:
[tex]\displaystyle 5\sin\theta\sec\theta=5\frac{\sin\theta}{\cos\theta}[/tex]
Substituting the definition of the tangent:
[tex]\displaystyle 5\sin\theta\sec\theta=5\tan\theta[/tex]
Correct choice D.
