Question

Trigonometric identities assignment 4

Answer 1

Answer:

Answer: choice D.

Step-by-step explanation:

Trigonometric Functions

We need to recall some properties and definitions of the trigonometric functions.

$\displaystyle \tan \theta=\frac{\sin\theta}{\cos\theta}$

$\displaystyle \sec \theta=\frac{1}{\cos\theta}$

We need to simplify the following expression:

$5\sin\theta\sec\theta$

Substituting the identity for the secant:

$\displaystyle 5\sin\theta\sec\theta=5\sin\theta.\frac{1}{\cos\theta}$

Operating:

$\displaystyle 5\sin\theta\sec\theta=5\frac{\sin\theta}{\cos\theta}$

Substituting the definition of the tangent:

$\displaystyle 5\sin\theta\sec\theta=5\tan\theta$

Correct choice D.