what is the formula of sin 3A and what are the formulae of all trigonometric functions and identities

Formula of sin 3A= sin 3A = 3 sin A − 4 sin³ A

List of Important Trigonometric Formulae

1. Basic Trigonometric Ratios

• sin A = Opposite / Hypotenuse
• cos A = Adjacent / Hypotenuse
• tan A = sin A / cos A = Opposite / Adjacent
• cot A = 1 / tan A
• sec A = 1 / cos A
• csc A = 1 / sin A

2. Pythagorean Identities

• sin² A + cos² A = 1
• 1 + tan² A = sec² A
• 1 + cot² A = csc² A

3. Double Angle Formulae

• sin 2A = 2 sin A cos A
• cos 2A = cos² A − sin² A = 2 cos² A − 1 = 1 − 2 sin² A
• tan 2A = (2 tan A) / (1 − tan² A)

4. Triple Angle Formulae

• sin 3A = 3 sin A − 4 sin³ A
• cos 3A = 4 cos³ A − 3 cos A
• tan 3A = (3 tan A − tan³ A) / (1 − 3 tan² A)

5. Sum and Difference Formulae

• sin(A ± B) = sin A cos B ± cos A sin B
• cos(A ± B) = cos A cos B ∓ sin A sin B
• tan(A ± B) = (tan A ± tan B) / (1 ∓ tan A tan B)

6. Product to Sum Formulae

• sin A sin B = ½ [cos(A − B) − cos(A + B)]
• cos A cos B = ½ [cos(A − B) + cos(A + B)]
• sin A cos B = ½ [sin(A + B) + sin(A − B)]

7. Half Angle Formulae

• sin²(A/2) = (1 − cos A) / 2
• cos²(A/2) = (1 + cos A) / 2
• tan(A/2) = sin A / (1 + cos A) = (1 − cos A) / sin A