COMEDK UGET 2026 Trigonometry Practice Questions with Solutions

The COMEDK UGET 2026 Mathematics section plays a crucial role in determining a candidate’s overall score, as it consists of 60 multiple-choice questions and contributes one-third of the total marks in the exam. The questions are generally based on the Class 11 and Class 12 syllabus and test conceptual clarity as well as speed in solving numerical problems. Within mathematics, Trigonometry is a recurring but moderate-weightage unit, typically contributing around 8–10% of the total maths questions, which means students can expect approximately 3–6 questions from this chapter in the exam. Because of its formula-based nature and direct application of identities, trigonometry is considered a scoring topic if students practice enough problems and revise formulas thoroughly.

The trigonometry portion in COMEDK mainly covers topics from the Class 11 and 12 syllabus. Some of the most important areas include trigonometric ratios and identities, trigonometric functions, properties of angles, inverse trigonometric functions, trigonometric equations, and graphs of trigonometric functions. Questions are also frequently asked from angle transformations, compound angles, multiple-angle identities, and trigonometric equations. Many problems require students to simplify expressions using identities or evaluate trigonometric values using standard formulas. Therefore, mastering formulas and understanding relationships between trigonometric functions becomes crucial while practicing COMEDK UGET trigonometry questions.

Based on previous year paper analysis, COMEDK tends to ask trigonometry questions that are concept-based but largely formula-driven. Most questions involve direct application of identities, solving trigonometric equations, evaluating expressions, or converting between trigonometric forms. In some cases, questions may be integrated with other topics such as limits, calculus, or coordinate geometry, which requires deeper conceptual understanding. Since the exam focuses on speed and accuracy, many questions are designed as short numerical problems that can be solved quickly if the formulas and identities are well remembered.

Looking at the last 3–4 years of COMEDK UGET exam trends, the difficulty level of trigonometry questions has generally been easy to moderate. Most problems are straightforward and based on standard identities or simple manipulations. However, some questions can be slightly time-consuming due to algebraic simplifications or multi-step calculations. Overall, students who are comfortable with basic trigonometric formulas and practice a wide range of problems usually find this section scoring. Solving COMEDK UGET 2026 Trigonometry practice questions with step-by-step solutions is therefore an effective way to strengthen concepts and become familiar with the type of questions frequently asked in the exam.

Also Check - Do or Die Chapters for COMEDK UGET 2026 Mathematics

COMEDK UGET 2026 Trigonometry Important Topics

Before starting with COMEDK Trigonometry practice questions, you should check the important topics mentioned in COMEDK UGET 2026 Mathematics syllabus . The Trigonometry chapter features various fundamental topics such as Positive and Negative angles, Trigonometric functions, Trigonometric identities, and signs of Trigonometric functions. In the following table, we have provided the complete list of topics in Trigonometry chapter for COMEDK UGET 2026:

COMEDK UGET 2026 Trigonometry Expected Weightage

Trigonometry in COMEDK UGET 2026 question paper features around 10-13% weightage with 6-8 questions. You should also check COMEDK UGET previous year question papers to identify which subtopic carries the highest and lowest weightages. You can check the detailed COMEDK UGET 2026 Trigonometry expected weightage here:

COMEDK UGET 2026 Trigonometry Practice Questions with Solutions

Once you are done covering the entire syllabus, test your knowledge and preparation level by solving COMEDK Trigonometry sample questions. These questions are almost accurate or similar to the questions asked in the examination. Our experts have compiled some of the most expected Trigonometry practice questions based on the past couple of years' paper trends. You can check the most important COMEDK UGET 2026 Trigonometry practice questions with solutions below:

Q1. If Sin A = 4/5 and Cos B = -12/13. Where A and B lie in the first and third quadrant respectively. Then Cos (A+B) =?

a. -16/65

b. 16/65

c. 65/16

d. -65/16

Ans. a. -16/65

Solution: We know that,

Cos (A+B) = CosA.CosB - SinA.SinB

First, we need to find the values of CosA and SinB

Since A lies in the first quadrant, both CosA and SinB are positive. We can use the Pythagorean identity to find CosA

Cos ² A + Sin ² A = 1

Substituting Sin A = 4/5

Cos ² A + (4/5) ² = 1

Cos ² A = 9/25 = CosA = 3/5

Since B lies in the third quadrant, both CosB and SinB are negative. We can again use the Pythagorean identity to find Sin B.

Cos ² B + Sin ² B = 1

Substituting Cos B = -12/13

(-12/13) ² + Sin ² B = 1

Sin ² B = 1-(144/169)

Sin ² B = 25/169 = SinB = - 5/13 (Negative sign because B is in third quadrant)

Now substituting all the values in Cos (A+B) = CosA.CosB - SinA.SinB

(3/5) (-12/13) – (4/5)(-5/13)

= -36/65 + 20/65 = -16/65

Q2. If Sin 2x = 4 cosx, then x is equal to

a. nⲡ/2 ± ⲡ/4, n ∊ Z

b. 2nⲡ ± ⲡ/2, n ∊ Z

c. nⲡ ± ⲡ/2, n ∊ Z

d. None of the above

Ans. b. 2nⲡ ± ⲡ/2, n ∊ Z

Solution: We have Sin 2x = 4 Cos x

2 SinxCosx = 4Cosx

Cos(Sin x -2) = 0

Cos x = 0 (Sin x ≠ 2)

Cos x = 0 = Cos ⲡ/2 = x = 2nⲡ ± ⲡ/2, n ∊ Z.

Q3. The function f(x) = tan ^-1 (Sin x + Cos x) is an increasing function in?

a. (ⲡ/4, ⲡ/2)

b. (0, ⲡ/2)

c. (-ⲡ/2, ⲡ/4)

d. (-ⲡ/2, ⲡ/2)

Ans. c. (-ⲡ/2, ⲡ/4)

Solution: To determine where the function f(x) = tan ^-1 (Sin x + Cos x) is increasing, we need to analyze its derivative. A function is increasing where its derivative is positive.

First, let's find the derivative of f(x). Given f(x) = tan ^-1 (sin x + cos x), from chain rule:

Let, u = sin x + cos x. Then, f(x) = tan ^-1 (u) and

d/dx[tan ^-1 (u)] = 1/(1+u ² )du/dx

Next, we calculate du/dx

u = sin x + cos x

So, du/dx = cos x - sin x

Thus, f’(x) = 1/[1+(sin x + cos x) ² ].(Cos x – Sin x)

To find where f’(x) > 0, examine the equation,

Cos x – Sin x > 0

Rewriting this, we have

Cos x > Sin x

To identify the intervals where Cos x > Sin x. let's take a look at the behavior of the basic trigonometric functions. We know that:

Cos x = Sin x, where x = ⲡ/4 + kⲡ for any integer k,

In the interval (-ⲡ/2, ⲡ/4), Cos x is generally greater than Sin x.

Verifying the intervals provided, we conclude that Cos x > Sin x holds true for x ∊ (-ⲡ/2, ⲡ/4),

Hence, the function, f(x) = tan-1(Sin x + Cos x) is an increasing function in (-ⲡ/2, ⲡ/4).

Q4. A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having a fence are of the same length x The maximum area enclosed by the park is:

a. √(x3/8

b. ⲡx2

c. 3/2x2

d. 1/2x2

Ans. d. 1/2x2

Solution: To determine the maximum area enclosed by the triangular park, we need to consider that the park is bound by two sides of equal length, x, and the third side by the river. One optimal configuration for maximum area in such cases is an isosceles triangle where the third side (formed by the river) is also a variable.

Let's denote the length of the third side by river as y. The angle between the two sides of length x will be Ө. The area of a triangle formed by two sides and the included angle is given by:

A = 1/2ab SinӨ

Where, a = x, b = x, are the sides of the park. Substituting values, we get,

A = 1/2 x ² SinӨ

To find the angle that maximizes SinӨ, and thus A, we note that SinӨ reaches the maximum value of 1, when Ө = 90°. This description provides for a right angle triangle. In this specific optimally configured triangle:

The base is x,

The height is x,

The angle between x and x is 90°. Thus the maximum area of the triangle will be,

Amax = 1/2x ² Sin90° = 1/2x ² (1) = 1/2x2.

Q5. If Sin 3Ө = Sin Ө, how many solutions exist such that, -2ⲡ < Ө < 2ⲡ

a. 9

b. 8

c. 7

d. 6

Ans. a. 9

Solution: Sin 3Ө = Sin Ө,

3Sin Ө – 4Sin3Ө = Sin Ө

4Sin3Ө – 2SinӨ = 0

2SinӨ (2Sin2Ө – 1) = 0

SinӨ = 0 or Sin Ө = ± 1/√2

If SinӨ = 0, and if SinӨ = ± 1/√2

Ө = 0, ⲡ, – ⲡ

Ө = ⲡ/4, 3ⲡ/4, –5ⲡ/4, –7ⲡ/4, –ⲡ/4, –3ⲡ/4, 5ⲡ/4, 7ⲡ/4

There are 9 solutions.

In addition to solving COMEDK important questions on Trigonometry, make it a habit to attempt mock tests regularly, at least twice or thrice a week. COMEDK UGET 2026 mock test will help you not only with practice and revision but also improve your time management skills and confidence level.

Previous Year Question Trends for Trigonometry in COMEDK UGET

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