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Chapter 5: Problem 10

Verify the identity. $$\sec y \cos y=1$$

Short Answer

Expert verified
The identity is proven.

Step by step solution

01

Understand the Reciprocal Relationship

Recall the definition of secant function. It is the reciprocal of the cosine function. This means, \( \sec y = \frac{1}{\cos y} \).
02

Substitute Secant With Its Definition

Substitute \(\sec y\) in the equation with its definition. Thus: \( \sec y \cos y = \frac{1}{\cos y} * \cos y \).
03

Simplify the Equation

Simplify the equation by cancelling out common factors. In this case, \(\cos y\) in the numerator and the denominator cancel out, thus: \( \frac{1}{\cos y} * \cos y = 1 \).

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