Class 10th & 12th Maths - Important Formulas & Theorems
1. Algebra (Algebraic Identities)
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
a² - b² = (a - b)(a + b)
(x + a)(x + b) = x² + (a + b)x + ab
2. Trigonometry (Important Ratios & Identities)
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
sin(A ± B) = sinA cosB ± cosA sinB
cos(A ± B) = cosA cosB ∓ sinA sinB
3. Geometry (Important Theorems)
Pythagoras Theorem: In a right-angled triangle, (Hypotenuse)² = (Base)² + (Height)²
The sum of all angles of a triangle is 180°
The opposite angles in a cyclic quadrilateral sum up to 180°
4. Probability & Statistics
Probability = (Favorable Outcomes) / (Total Outcomes)
Mean = (Sum of all observations) / (Total number of observations)
Median = Middle value of an arranged dataset
Mode = Most frequently occurring value in a dataset
1. Algebra (Algebraic Identities)
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
a² - b² = (a - b)(a + b)
(x + a)(x + b) = x² + (a + b)x + ab
2. Trigonometry (Important Ratios & Identities)
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
sin(A ± B) = sinA cosB ± cosA sinB
cos(A ± B) = cosA cosB ∓ sinA sinB
3. Geometry (Important Theorems)
Pythagoras Theorem: In a right-angled triangle, (Hypotenuse)² = (Base)² + (Height)²
The sum of all angles of a triangle is 180°
The opposite angles in a cyclic quadrilateral sum up to 180°
4. Probability & Statistics
Probability = (Favorable Outcomes) / (Total Outcomes)
Mean = (Sum of all observations) / (Total number of observations)
Median = Middle value of an arranged dataset
Mode = Most frequently occurring value in a dataset
