In Class 11 Mathematics (Trigonometry), mastering the 'Triple Angle Formulas' is essential for solving complex algebraic proofs and calculus problems. The formula for tan(3x) connects the tangent of a triple angle entirely to the tangent of a single angle.
Unlike the sin(3x) and cos(3x) formulas which don't have denominators, the tan(3x) formula is a rational fraction because tan(x) itself is a ratio (sin/cos).
The complete formula for tan(3x) is:
tan(3x) = (3tan x - tan³x) / (1 - 3tan²x)
(You can also write it using theta: tan(3θ) = (3tanθ - tan³θ) / (1 - 3tan²θ)).
Notice the pattern of the numbers 3 and 1:
3 and power of 3: (3tan x - tan³x)1 and ends with 3 and square: (1 - 3tan²x)To prove this formula, you use the standard addition formula: tan(A + B).
No. Like all tangent functions, it is undefined (tends to infinity) when the denominator becomes zero, or when x = π/2, 3π/2, etc., because tan(90°) is undefined.
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