Answer:
Correct choice D.
Step-by-step explanation:
Trigonometric Identities
We need to recall some properties and definitions of the trigonometric functions.
[tex]\tan \theta=\frac{\sin\theta}{\cos\theta}[/tex]
[tex]\sec \theta=\frac{1}{\cos\theta}[/tex]
It's required 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]
Now we use the definition of the tangent:
[tex]\displaystyle 5\sin\theta\sec\theta=5\tan\theta[/tex]
Correct choice D.
