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Trigonometric identities assignment 4

Simplify 5 sin ø sec ø

A. 5 cot ø
B. 5
C. 5 cos ø
D. 5 tan ø

Trigonometric identities assignment 4 Simplify 5 sin ø sec ø A. 5 cot ø B. 5 C. 5 cos-example-1
User Rvanlaak
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8.4k points

1 Answer

12 votes

Answer:

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.

User MoreScratch
by
8.9k points
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