To prove the equation tan(3x) tan(2x) tan(x) = tan(3x) tan(2x) tan(x), we observe that both sides of the equation are identical. Therefore, no additional proof is necessary as both sides represent the same mathematical expression.
To further understand this, let’s consider the three separate tangent functions:
- tan(3x): This is the tangent of the angle multiplied by three.
- tan(2x): This is the tangent of the angle multiplied by two.
- tan(x): This is the tangent of the angle itself.
Since we are demonstrating an equality between the left-hand side and the right-hand side of the equation, the proof is straightforward; hence, we can conclude that:
tan(3x) tan(2x) tan(x) = tan(3x) tan(2x) tan(x) is inherently true, as it states that a multiplication of terms equals itself.