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Proof: Tangent Quotient Identity

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\tan \theta = \frac{\sin \theta}{\cos \theta}



Definition of Tangent:

\tan \theta = \frac{\mathrm{opposite}}{\mathrm{adjacent}}

\tan \theta = \frac{\mathrm{opposite}}{\mathrm{adjacent}} \cdot 1

\tan \theta = \frac{\mathrm{opposite}}{\mathrm{adjacent}} \cdot \frac{\mathrm{hypotenuse}}{\mathrm{hypotenuse}}

\tan \theta = \frac{ \frac{\mathrm{opposite}}{\mathrm{hypotenuse}}}{\frac{ \mathrm{adjacent}}{\mathrm{hypotenuse}}}

Definition of Sine and Cosine:

\tan \theta = \frac{\sin \theta}{\cos \theta}

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