Chapter 7.4, Problem 7AYU

True or False In establishing an identity, it is often easiest to just multiply both sides by a well-chosen nonzero expression involving the variable.

To determine

To find: Check whether the given statement is true or false: In establishing an identity, it is often easiest to just multiply both by a well-chosen non-zero expression involving the variable.

Answer to Problem 7AYU

Solution:

True. In establishing an identity, it is often easiest to just multiply both by a well-chosen non-zero expression involving the variable.

Explanation of Solution

Given:

In establishing an identity, it is often easiest to just multiply both by a well-chosen non-zero expression involving the variable.

Calculation:

Trigonometric identity $1+{\text{tan}}^2\theta = {\text{sec}}^2\theta$.

$1+{\text{tan}}^2\theta = {\text{sec}}^2\theta$

By quotient Identity

$1+\frac{{\text{sin}}^2\theta }{{\text{cos}}^2\theta }=\frac{1}{{\text{cos}}^2\theta }$

Multiply by ${\text{cos}}^2\theta$.

Pythagorean identity

${\text{cos}}^2\theta +{\text{sin}}^2\theta =1$