Trigonometry Formulas for Class 12 – All Important Formulas

What if we told you there’s a chapter in class 12 Maths that keeps showing up across topics, understanding which makes everything else easier? Yes, we’re talking about Trigonometry! And the first step to grasp it is learning all the Trigonometry formulas for Class 12.

Memorising these formulas will help you score higher in your CBSE Maths board exam and strengthen your base for Physics and various competitive exams. That’s why learning it is not just helpful, it’s necessary. In this blog, we’ll take you through all the Trigonometry formulas for Class 12, including key Trigonometric identities Class 12, and step-by-step solved examples to help you revise and apply them easily.

All Trigonometry Formulas For Class 12

Looking for a complete, easy-to-revise, and well-explained list of Trigonometry formulas for Class 12? You’ve landed in the right place. Below is a breakdown of all trigonometric formulas, identities, and functions covered under the CBSE Class 12 Maths syllabus. These are perfect for quick revision so that you can score well in both board exams and competitive entrances.

1. Trigonometric Ratios

Trigonometry starts by studying ratios in a right-angled triangle, and the entire chapter is based on how the angles relate to the triangle’s sides. In a right-angled triangle:

• Height (or perpendicular) is the side opposite the angle.
• The base is the side adjacent (next to) the angle.
• Hypotenuse is the longest side, always opposite the right angle.

These three sides help define the six trigonometric ratios and are used to find unknown angles or sides in triangle-based problems. The ratios have been summed up in the table below:

The standard Trigonometric table with common angle values has also been stated below:

2. Trigonometric Identities

These equations are valid for all angle values and are widely used to simplify expressions and solve equations. The area of Trigonometric identities class 12 is highly tested in CBSE boards and other competitive exams. Moreover, you can directly head down to the next sub-heading to understand the difference between Trigonometric ratios and identities. 

The Trigonometry formulas for class 12 from this chapter are stated as follows:

Fundamental Identities:

• Sin^⁡2θ + cos⁡²θ = 1
• 1 + tan⁡²θ = sec⁡²θ
• 1 + cot⁡²θ = cosec^⁡2θ

Double Angle Identities:

• Sin⁡2θ = 2 sin⁡θcos⁡θ
• Cos⁡2θ = cos⁡²θ − sin⁡²θ = 2cos⁡²θ − 1 =1−2sin²θ
• Tan⁡2θ = 2 tan⁡θ/1−tan⁡²θ

Triple Angle Identities:

• Sin⁡3θ = 3sin⁡θ − 4sin⁡³θ
• Cos⁡3θ = 4cos^⁡3θ − 3cos⁡θ
• Tan⁡3θ = 3tan⁡θ − tan⁡³θ/1−3tan⁡²θ

3. Inverse Trigonometric Formulas

Inverse trigonometric functions are used when the angle is the unknown. This chapter usually carries 4 marks in CBSE and often appears in calculus, particularly in integrals and differential equations. The Trigonometry formulas for class 12 from this chapter are stated as follows:

Basic Inverse Relationships:

• Sin⁡⁻¹x + cos⁡⁻¹x = π/2
• Tan^⁡−1x+cot⁡⁻¹x = π/2
• Sec⁡⁻¹x+cosec⁡⁻¹x = π/2

Compound Angle Identities:

Twice and thrice of inverse Trigonometric functions:

• 2tan^-1 A = sin^-1(2A / (1 + A²)), |A| ≤ 1
• 2tan^-1 A = cos^-1((1 – A²) / (1 + A²)), A ≥ 0
• 2tan^-1 A = tan^-1(2A / (1 – A²)), -1< A <1
• 3sin^-1 A = sin^-1(3A – 4A³)
• 3cos^-1 A = cos^-1(4A³ – 3A)
• 3tan^-1 A = tan^-1((3A – A³)/(1 – 3A²))

Domain and Range of inverse Trigonometric functions: 

4. Height and Distance

The chapter Height and Distance focuses on the practical applications of Trigonometry in real-life contexts. It deals with problems involving angles of elevation and depression, where trigonometric ratios are used to calculate unknown heights or distances. In CBSE Class 12, this topic carries 3 to 5 marks and often appears as short answers or application-based questions. A few concepts and the Trigonometry formulas for Class 12 from this portion have been listed below:

• Angle of elevation: If you’re looking upward at an object, the angle formed with the horizontal is called the angle of elevation. It can be denoted using the formula below:

Tan⁡(θ) = Height of object/Horizontal distance from observer

• Angle of depression: If you’re looking downward from a height, the angle formed with the horizontal is called the angle of depression. It can be denoted using this formula of Trigonometry class 12:

tan⁡(θ) = Height from eye level/Horizontal distance to object

• Two objects seen from a point: When two objects are viewed from a single point at two different angles (e.g., top and bottom of a tower or balloon):

H = d⋅tan⁡A⋅tan⁡B/tan⁡A−tan⁡B

• When two angles are given from two points on the same line: Write two tan equations and solve for height or distance.

For example, h = d⋅tan⁡(θ)

H = (d+x)⋅tan⁡(α), then solve for unknowns.

• Heights of shadows: 

Tan⁡θ = Length of shadow/Height of object (when the sun’s angle of elevation is given)

• Pythagorus theorem:Hypotenuse² = base² + height²

Now that you’ve gone through all the Trigonometry formulas for class 12 listed above under each subheading, compiling them into a single PDF is a smart idea. You can also print it out as your go-to formula sheet for a quick revision before every exam. 

Also Learn: Chapter-wise Maths Formulas for Class 12

Difference Between Trigonometric Identities And Trigonometric Ratios

Let’s understand the basic definition of both Trigonometric identities and ratios. Next, we will also help you understand both using an example. So, Trigonometric ratios are the basic relationships between the angles and sides of a right-angled triangle. These include sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec), and cotangent (cot). Thus, they form the basics of all Trigonometry formulas for class 12.

On the other hand, Trigonometric identities class 12 are proven relationships that simplify complex expressions and, in turn, are used to solve equations. So, let’s say you’re standing next to a tall building and want to find its height. You know the distance from the base and the angle of elevation. In this case, you’d use a trigonometric ratio like tan(θ) = height/base to find the unknown side.

To simplify a complex expression or solve an equation during that process, you might use a Trigonometric identity such as sin²θ + cos²θ = 1. In short, Trigonometric ratios are used to calculate, while trigonometric identities help you simplify. Both are important sub-parts and appear in the CBSE board exam. 

That’s it! These are all the Trigonometry formulas for class 12 you need to focus on. Once you’ve memorised them and practised solving different types of questions using them, you’re already halfway to scoring full marks. Next, we’ll look at a few simple examples to get you started.

Also Learn: Chapter-wise Physics Formulas for Class 12

Class 12 Maths Solved Examples Based on Trigonometry

Now that we’ve shared the Trigonometry Class 12 all formulas, let’s jump into some problem-based sums with answers. Take out your notebook and pen, and start solving. Try to work through each question first, then check your answers using the solutions provided. 

Example 1: Solve sin ⁡75° 

Solution:

Break 75° as 45°+30° and use the formula:

sin⁡(A+B) = sin ⁡A cos⁡ B + cos A sin ⁡B

sin 75° = sin(45°+30°)

= sin 45° cos 30° + cos 45° sin 30°

Answer:

Example 2: If cos ⁡θ =⅗ and θ is acute, find the values of the other trigonometric ratios.

Solution:

Given cos ⁡θ = ⅗ , let base = 3, hypotenuse = 5.

Using Pythagoras theorem: 

Hypotenuse² = base² + height²

Substituting the values,

5² = 3² + height²

25 = 9 + height²

Height² = 9 – 25 = 16 

Height = 4 

Now, find the remaining trigonometric ratios:

• Formula used: cos ⁡A = Base/Hypotenuse = ⅘ 
• Tan ⁡A = Opposite/Base = ¾
• Sec⁡ A = 1/cos⁡ A = 5/4 
• Cosec⁡ A = 1/sin⁡A = 5/3  
• Cot⁡ A = Base/Opposite = 4/3 

Example 3: Prove: 

Solution:

Let’s start by solving LHS:

Multiply the numerator and denominator by (sec⁡ A + tan ⁡A)

Formula used: a² − b² = (a−b)(a+b)

Use identity: sec⁡² A − tan⁡²A = 1, so it becomes:

sec⁡²A + tan⁡²A + 2 sec⁡ A tan ⁡A  = RHS 

Example 4: From the top of a building 30 m high, the angles of depression to two cars parked in the same line are 30° and 60°. Find the distance between the two vehicles.

Solution:

Let the distances from the foot of the building to car A and car B be xx and yy.

Formula used: tan ⁡θ = Opposite/Adjacent

Distance between cars = x−y = 30√3 − 10√3

Answer: 20√3 m

Must Buy: CBSE Class 12 Question Banks for 2026 Exam Preparation

Conclusion

Trigonometry is not as tough as it sounds. Once you get the hang of it, it’s one of the easiest and most scoring topics in CBSE class 12. And guess what makes it even simpler? Knowing your Trigonometry formulas for class 12 at the back of your hand.

Every formula of Trigonometry class 12 helps you work smarter, not harder. But just knowing them isn’t enough; you must practice them regularly. So, solve different types of questions, revise using your formula sheet, and test yourself as often as possible. Follow this approach consistently; you won’t just understand Trigonometry, you’ll score full marks! 

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