Chapter 13.3, Problem 42HP

To determine

To verify: The given conclusion is true for the specific values.

Explanation of Solution

Given:

A,B,C are angle of the oblique triangle. Then:

  $\tan A+\tan B+\tan C=\tan A\tan B\tan C$

Since, the angle A,B,C are the angle of the triangle then their sum will be equal to the 1800-degree.

Considering the value of them as shown below:

  $A={45}^o,B={60}^o,C={75}^o$

Considering the Left hand side of the given expression:

  $\begin{array}{c}\tan A+\tan B+\tan C=\tan {45}^o+\tan {60}^o+\tan {75}^o\\ =1+11.732+3.732\\ =6.464\end{array}$

Now, considering the Right hand side of the given expression:

  $\begin{array}{c}\tan A.\tan B.\tan C=\tan {45}^o.\tan {60}^o.\tan {75}^o\\ =1\times 1.732\times 3.732\\ =6.464\end{array}$

From the above results, it is clear that the left hand side is equal to the right hand side

Therefore, the theorem is true and verified.