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Prove the trigonometric identity for
Solution:
The first thing that you have to do is to examine the both sides of the equation and look for the more complicated side. In this case, the left side of the equation is more complicated. Let's simplify the left side of the equation as follows
The left side of the equation is the sum of two angles of tangent function. Let's apply the sum of two angles formula for tangent function as follows
Since each trigonometric functions at each term of the equation are inverse functions to each other, then we can cancel the tangent and inverse tangent functions at each term as follows
Therefore,
