Chapter 7.4, Problem 108AYU

To determine

Make up an identity that is not a Fundamental Identity.

Answer to Problem 108AYU

Yes they are treated as identity.

Explanation of Solution

Given information:

Make up an identity that is not a Fundamental Identity.

Calculation:

As we know that if an equation is said to be balanced different values of angles then it is treated as an identity.

There are so many equations which can be treated as identity.

For example:

  $\begin{array}{l}\left(\cos ec\theta -\cot \theta \right)\left(\cos ec\theta +\cot \theta \right)=1\\ \left(1-{\cos }^2\theta \right)\left(1+{\cot }^2\theta \right)=1\\ \left(9{\sec }^2\theta -5{\tan }^2\theta \right)=5+4{\sec }^2\theta \end{array}$

If we substitute differnt values of angles we will see that they will satisfy the equation.

Hence, they are treated as identity.