Question Video: Using the Tangent Sum or Difference of Angles Identity to Simplify a Trigonometric Expression Mathematics

Simplify (tan 33° + tan 299°)/(1 − (tan 33° tan 299°)).

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Video Transcript

Simplify tan of 33 degrees plus tan of 299 degrees all over one minus tan of 33 degrees times the tan of 299 degrees.

The key to simplifying this expression is recognizing the pattern here. Two of these tangent values are 33 degrees, and two of the values are 299 degrees, which means this expression is in the form the tan of 𝐴 plus the tan of 𝐵 all over one minus the tan of 𝐴 times the tan of 𝐵. And this pattern is an angle sum identity. It’s equal to the tan of 𝐴 plus 𝐵.

For our expression, we can let 33 degrees be equal to 𝐴 and 299 degrees be equal to 𝐵, which means this simplifies to the tan of 33 degrees plus 299 degrees, which is the tan of 332 degrees. Our instructions have just been to simplify and not to calculate. So, we say that the simplified form of the expression that we started with is the tan of 332 degrees.

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