Questions: Simplify tan(t) / sec(t) to a single trig function with no fractions.

Simplify tan(t) / sec(t) to a single trig function with no fractions.
Transcript text: Assignment 7.1: Solving Trigonometric Equations with Ide Assignment 7.1: Solving Trigonometric Equatio Score: 1/13 Answered: 1/13 Question 2 Simplify $\frac{\tan (t)}{\sec (t)}$ to a single trig function with no fractions. $\square$ Question Help: Video Submit Question
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Solution

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Solution Steps

Step 1: Express \(\tan(t)\) and \(\sec(t)\) in terms of sine and cosine

\[ \tan(t) = \frac{\sin(t)}{\cos(t)}, \quad \sec(t) = \frac{1}{\cos(t)} \]

Step 2: Substitute the expressions into the original equation

\[ \frac{\tan(t)}{\sec(t)} = \frac{\frac{\sin(t)}{\cos(t)}}{\frac{1}{\cos(t)}} \]

Step 3: Simplify the fraction

\[ \frac{\frac{\sin(t)}{\cos(t)}}{\frac{1}{\cos(t)}} = \sin(t) \]

Final Answer

\(\boxed{\sin(t)}\)

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