For a right-angled triangle:
• sin θ = Opposite / Hypotenuse
• cos θ = Adjacent / Hypotenuse
• tan θ = Opposite / Adjacent
• cosec θ = 1 / sin θ
• sec θ = 1 / cos θ
• cot θ = 1 / tan θ
2. Pythagorean Identities
• sin²θ + cos²θ = 1
• 1 + tan²θ = sec²θ
• 1 + cot²θ = cosec²θ
3. Reciprocal Identities
• cosec θ = 1/sin θ
• sec θ = 1/cos θ
• cot θ = 1/tan θ
4. Co-Function (Complementary Angle) Identities
• sin(90° - θ) = cos θ
• cos(90° - θ) = sin θ
• tan(90° - θ) = cot θ
• cot(90° - θ) = tan θ
• sec(90° - θ) = cosec θ
• cosec(90° - θ) = sec θ
5. Negative Angle Identities
• sin(-θ) = -sin θ
• cos(-θ) = cos θ
• tan(-θ) = -tan θ
• cot(-θ) = -cot θ
• sec(-θ) = sec θ
• cosec(-θ) = -cosec θ
6. Sum and Difference Formulas
• 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)
7. Double Angle Formulas
• sin 2A = 2 sin A cos A
• cos 2A = cos²A - sin²A = 2cos²A - 1 = 1 - 2sin²A
• tan 2A = 2 tan A / (1 - tan²A)
8. Half Angle Formulas
• sin(A/2) = ±√[(1 - cos A) / 2]
• cos(A/2) = ±√[(1 + cos A) / 2]
• tan(A/2) = ±√[(1 - cos A) / (1 + cos A)]
9. Product to Sum Formulas
• sin A sin B = 1/2 [cos(A - B) - cos(A + B)]
• cos A cos B = 1/2 [cos(A + B) + cos(A - B)]
• sin A cos B = 1/2 [sin(A + B) + sin(A - B)]
10. Sum to Product Formulas
• sin A + sin B = 2 sin[(A + B)/2] cos[(A - B)/2]
• sin A - sin B = 2 cos[(A + B)/2] sin[(A - B)/2]
• cos A + cos B = 2 cos[(A + B)/2] cos[(A - B)/2]
• cos A - cos B = -2 sin[(A + B)/2] sin[(A - B)/2]
11. Inverse Trigonometric Identities
• sin⁻¹(-x) = -sin⁻¹x
• cos⁻¹(-x) = π - cos⁻¹x
• tan⁻¹(-x) = -tan⁻¹x
• sin⁻¹x + cos⁻¹x = π/2
• tan⁻¹x + cot⁻¹x = π/2
• sec⁻¹x + cosec⁻¹x = π/2
