Question

Trigonometric identities assignment 4

Simplify 5 sin ø sec ø

A. 5 cot ø
B. 5
C. 5 cos ø
D. 5 tan ø

Answer 1

Answer: choice D.

Explanation:

Trigonometric Functions

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

`\displaystyle \tan \theta=(\sin\theta)/(\cos\theta)`

`\displaystyle \sec \theta=(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.(1)/(\cos\theta)`

Operating:

`\displaystyle 5\sin\theta\sec\theta=5(\sin\theta)/(\cos\theta)`

Substituting the definition of the tangent:

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

Correct choice D.