Algebra and Trigonometry Formula Guide for SSC Exams
Rahul Kumar
SSC Exam Expert & Content Editor
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Algebra and trigonometry give many easy marks in SSC maths if you know the identities and the value table. This algebra and trigonometry formula guide for SSC collects the algebraic identities, the quadratic formulas, the trigonometric ratios and identities, and the standard angle values in clear tables with solved examples.
Algebraic Identities
| Identity | Formula |
|---|---|
| (a + b)² | a² + 2ab + b² |
| (a − b)² | a² − 2ab + b² |
| a² − b² | (a + b)(a − b) |
| (a + b)³ | a³ + 3a²b + 3ab² + b³ |
| (a − b)³ | a³ − 3a²b + 3ab² − b³ |
| a³ + b³ | (a + b)(a² − ab + b²) |
| a³ − b³ | (a − b)(a² + ab + b²) |
| (a + b + c)² | a² + b² + c² + 2(ab + bc + ca) |
| a³ + b³ + c³ − 3abc | (a + b + c)(a² + b² + c² − ab − bc − ca) |
If a + b + c = 0, then a³ + b³ + c³ = 3abc. Also a² + b² = (a + b)² − 2ab.
Quadratic Equation
| Item | Formula |
|---|---|
| Equation | ax² + bx + c = 0 |
| Roots | x = [−b ± √(b² − 4ac)] / 2a |
| Sum of the roots | −b / a |
| Product of the roots | c / a |
| Discriminant D | b² − 4ac; real and different roots if D is positive, equal roots if D is zero, no real roots if D is negative |
Trigonometric Ratios
- sin θ = perpendicular / hypotenuse
- cos θ = base / hypotenuse
- tan θ = perpendicular / base
- cosec θ = 1 / sin θ, sec θ = 1 / cos θ and cot θ = 1 / tan θ
- tan θ = sin θ / cos θ
Trigonometric Identities
| Identity | Formula |
|---|---|
| 1 | sin²θ + cos²θ = 1 |
| 2 | 1 + tan²θ = sec²θ |
| 3 | 1 + cot²θ = cosec²θ |
| Complementary angles | sin(90° − θ) = cos θ and tan(90° − θ) = cot θ |
Standard Angle Values
| Angle | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cos | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| tan | 0 | 1/√3 | 1 | √3 | Not defined |
Solved Examples
Example 1. If a + b = 5 and ab = 6, find a² + b².
a² + b² = (a + b)² − 2ab = 25 − 12 = 13.
Example 2. Find the sum and the product of the roots of x² − 5x + 6 = 0.
The sum is 5 and the product is 6.
Example 3. Find the value of sin 30° + cos 60°.
1/2 + 1/2 = 1.
Quick Tips
- Learn the angle value table by the pattern: sin goes 0, 1/2, 1/√2, √3/2, 1.
- Cos is the reverse order of sin.
- Use a² + b² = (a + b)² − 2ab in many questions.
- Remember that a + b + c = 0 gives a³ + b³ + c³ = 3abc.
Quick Revision Points
- (a + b)² = a² + 2ab + b².
- a² − b² = (a + b)(a − b).
- The sum of the roots is −b/a and the product is c/a.
- sin²θ + cos²θ = 1.
- sin 30° = 1/2 and tan 45° = 1.
Practice Questions With Answers
- Find (a + b)² when a = 3 and b = 2.
Answer: 25 - If a + b = 5 and ab = 6, find a² + b².
Answer: 13 - Factorise a² − b².
Answer: (a + b)(a − b) - If a + b + c = 0, find a³ + b³ + c³.
Answer: 3abc - Find the sum of the roots of x² − 5x + 6 = 0.
Answer: 5 - Find the product of the roots of x² − 5x + 6 = 0.
Answer: 6 - Find the value of sin 30°.
Answer: 1/2 - Find the value of tan 45°.
Answer: 1 - Find the value of sin²θ + cos²θ.
Answer: 1 - Find the value of cos 60°.
Answer: 1/2
How to Practise This Chapter
Write each formula on a card, with a solved example on the back, and revise the cards every day. Then test yourself with our practice papers and the previous year papers page. See all guides on the Formula Guide page, and also read the Mathematics notes and Quantitative Aptitude notes. The previous guide is Geometry and Mensuration and the next guide is Statistics and Probability.
Frequently Asked Questions
What is the formula for (a + b) squared?
It is a squared plus 2ab plus b squared.
What is the formula for a squared minus b squared?
It is (a + b) times (a minus b).
What is a plus b plus c equal to zero used for?
If a + b + c = 0, then a cubed plus b cubed plus c cubed equals 3abc.
What are the roots of a quadratic equation?
They are given by minus b plus or minus the root of (b squared minus 4ac), divided by 2a.
What is the sum of the roots?
The sum of the roots is minus b divided by a.
What is the product of the roots?
The product of the roots is c divided by a.
What is sin squared plus cos squared?
It is always equal to 1.
What is the value of sin 30 degrees?
It is 1/2.
What is the value of tan 45 degrees?
It is 1.
Is trigonometry important for SSC exams?
Yes. Trigonometry has a fixed number of questions in the SSC CGL and CHSL maths papers.
How can I remember the angle values?
Learn the pattern: sin values go 0, 1/2, 1/root 2, root 3/2 and 1, and the cos values go in the reverse order.
How many questions come from this topic in SSC exams?
Usually three to six questions, but the number changes from exam to exam.
Previous chapter
Geometry and Mensuration Formula Guide for SSC Exams
Next chapter
Statistics and Probability Formula Guide for SSC Exams
Rahul Kumar
SSC Exam Expert & Content Editor
Rahul is a senior SSC exam strategist with 8+ years of experience helping aspirants crack CGL, CHSL and MTS exams. He writes in-depth notification breakdowns, exam pattern guides and preparation strategies.