### Video Transcript

Simplify tan of 118 degrees minus two π plus tan of 32 degrees plus two π all over one minus tan of 118 degrees minus two π times tan of 32 degrees plus two π.

To simplify this, weβll need to recognize a pattern. To help us recognize this pattern, weβre going to take whatβs in the parentheses and represent that as a variable. We can say that π equals 118 degrees minus two π and that π¦ equals 32 degrees plus two π.

Weβll then have something like this, the tan of π plus the tan of π¦ over one minus tan π times tan π¦. And this is a form of a trig identity. Itβs a form of tan of πΌ plus π½. Tan of πΌ plus π½ equals tan of πΌ plus tan of π½ over one minus tan of πΌ times tan of π½. If we apply that to our expression, we can simplify it to say tan of π plus π¦.

Weβll take our values for π and π¦ and plug them back in. And now we have tan of 118 degrees minus two π plus 32 degrees plus two π. Minus two π plus two π cancels out. 118 degrees plus 32 degrees equals 150 degrees. Tan of 150 degrees is equal to negative square root of three over three.

The most simplified form of this expression is negative square root of three over three.