Use a Sum or Difference Identity to Find the Exact $\tan 105 ^ { \circ }$

question 378

Multiple Choice

Use a sum or difference identity to find the exact value.
- $\tan 105 ^ { \circ }$

• A) \(\frac { 2 + \sqrt { 3 } } { 4 }\)
• B) \(2 + \sqrt { 3 }\)
• C) \(\frac { 2 - \sqrt { 3 } } { 4 }\)
• D) \(- 2 - \sqrt { 3 }\)

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Definitions:

Quintet

A group of five lines or peaks observed close together in a spectroscopic measurement, often indicative of a specific atomic or molecular structure.

Triplet

In spectroscopy, a pattern of three closely spaced spectral lines or signals, often due to splitting in NMR or EPR spectroscopy caused by spin-spin coupling.

Signals

Manifestations or indicators that convey information or data, especially within the context of communication systems or analytical instrumentation.

Diastereotopic

Describes hydrogen atoms or groups in a molecule that are not equivalent in the three-dimensional structure, leading to different stereochemical outcomes.