Question

Use the sum and difference identities to determine the exact value of the following expression. If the answer is undefined, write DNE.tan17724tan1110241751 + tantan1172424

Answer 1

The Solution:

Given the expression below:

We are required to determine the exact value of the above expression.

Recall:

By Trigonometric identity,

$\frac{\:tan\left(\frac{17\pi\:}{24}\right)-tan\left(\frac{11\pi\:}{24}\right)}{1+\:tan\left(\frac{17\pi\:}{24}\right)tan\left(\frac{11\pi\:}{24}\right)}=\tan (\frac{17\pi}{24}-\frac{11\pi}{24})$

This becomes:

$\tan (\frac{17\pi}{24}-\frac{11\pi}{24})=\tan (\frac{17\pi-11\pi}{24})=\tan (\frac{6\pi}{24})=1$$undefined$

Therefore, the correct answer is 1