Learn formula of cot (3x) or cot (3A) or cot (3θ) or cot (3α) identity with introduction and geometric proof to expand or simplify cot of triple angle.

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To prove the triple-angle identities, we can write \sin 3 \theta sin3θ as \sin (2 \theta + \theta) sin(2θ+θ). Then we can use the sum formula and the double-angle identities to get the desired form:

L.H.S = 3–9tan2A 3tanA–tan3A 3 – 9 t a n 2 A 3 t a n A – t a n 3 A L.H.S = 3 (1–3tan2A 3tanA–tan3A 1 – 3 t a n 2 A 3 t a n A – t a n 3 A) Since 3tanA–tan3A 1–3tan2A 3 t a n A – t a n 3 A 1 – 3 t a n 2 A = tan 3A L.H.S = 3 tan3A 3 t a n 3 A = 3 cot 3A = R.H.S

Prove the following-$\\cot 3 {\\text {A}} = \\dfrac { {3cotA - { {\\cot }^3} {\\text {A}}}} { {1 - 3 { {\\cot }^2} {\\text {A}}}}$. Ans: Hint: We need to convert the multiples angle into half angles in this question. As we can see, cot3A is being written in terms...

When the height and base side of the right triangle are known, we can find out the sine, cosine, tangent, secant, cosecant, and cotangent values using trigonometric formulas. The reciprocal trigonometric identities are also derived by using the trigonometric functions.

The trigonometric triple-angle identities give a relationship between the basic trigonometric functions applied to three times an angle in terms of trigonometric functions of the angle itself. Triple-angle Identities.

Jul 18, 2014 · Chapter : Trigonometric Ratios Upto Transformations Lesson : Trigonometric Ratios Of Multiple & Sub-Multiple Angles...more.

Cot 3A calculator uses Cot 3A = (3*Cot A-Cot A^3)/ (1-3*Cot A^2) to calculate the Cot 3A, The Cot 3A formula is defined as the trigonometric cotangent function of thrice the given angle A.

Mar 2, 2025 · To prove the given trigonometric identity, let's follow the steps carefully: We start with the condition given in the problem: A + B + C = πc. Our goal is to prove the identity: cot(3A) ⋅ cot(3B) +cot(3B) ⋅ cot(3C) + cot(3A) ⋅ cot(3C) = 1. Simplify Each Term: Simplify the cotangent terms cot(3(πc − A − B)).