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On November 8, 2012, we derived the formulas for Sine Law and Cosine Law. Right now, we will derive the formula for Tangent Law. Let's consider the formula for Sine Law:
In this derivation, we will use only the first two terms of the given equation above. Let's have this one
Arrange the above equation, we have
Add 1 on both sides of the equation and simplify
Subtract 1 on both sides of the equation and simplify
Divide equation 1 by equation 2
At the right side of the equation, use the Sum and Product of Two Angles Formula to convert the sum of the two angles into the product of two angles, we have
Therefore,
If you will derive using the other term of Sine Law, the other formulas of Tangent Law will be
