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,

`(\:tan\left((17\pi\:)/(24)\right)-tan\left((11\pi\:)/(24)\right))/(1+\:tan\left((17\pi\:)/(24)\right)tan\left((11\pi\:)/(24)\right))=\tan ((17\pi)/(24)-(11\pi)/(24))`

This becomes:

`\tan ((17\pi)/(24)-(11\pi)/(24))=\tan ((17\pi-11\pi)/(24))=\tan ((6\pi)/(24))=1`

Therefore, the correct answer is 1