Question

Trigonometric identities assignment 4

Answer 1

Answer:

D. 5 tan ø

Step-by-step explanation:

$5 \sin \phi \: \sec \phi \\ \\ = 5 \sin \phi \: \times \frac{1}{ \cos \phi} \\ \\ = 5 \frac{\sin \phi}{ \cos \phi} \\ \\ = 5 \tan \phi$

Answer 2

Answer:

Correct choice D.

Step-by-step explanation:

Trigonometric Identities

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

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

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

It's required 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:

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

Now we use the definition of the tangent:

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

Correct choice D.