Trigonometry for CUET UG GAT

Trigonometry – Complete Guide for CUET UG GAT 2026 | MCQs, Tricks, Patterns & Solutions

Introduction to Trigonometry

Trigonometry for CUET UG GAT is one of the most important branches of mathematics that deals with the relationships between the angles and sides of triangles. It plays a crucial role in solving problems related to geometry, height and distance, navigation, physics, engineering, and competitive exams.

For CUET UG GAT 2026, Trigonometry is a high-scoring topic because questions are usually formula-based and can be solved quickly using proper techniques and shortcuts.

Understanding trigonometric identities, angles, and ratios helps students solve complex problems efficiently and improve overall exam performance.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies the relationship between the sides and angles of triangles, especially right-angled triangles.

The word Trigonometry comes from:

Tri = Three
Gon = Angle
Metry = Measurement

So, Trigonometry means:

“Measurement of triangles.”

Basic Trigonometric Ratios

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

Important Trigonometric Identities

sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ

tan θ = sin θ / cos θ
cot θ = cos θ / sin θ

Why Trigonometry is Important for CUET UG GAT 2026?

Frequently asked topic in Trigonometry for CUET UG GAT aptitude section
Easy scoring with formula-based questions
Improves problem-solving speed
Required for higher mathematics topics
Helps in geometry and quantitative aptitude

Expected Weightage in Trigonometry for CUET UG GAT section:
1 to 2 Questions

Common Patterns of Questions in Trigonometry for CUET UG GAT

Basic trigonometric ratios
Trigonometric identities
Standard angle values
Simplification problems
Height and distance problems
Complementary angle identities
Reciprocal identities

Short Tricks to Solve Trigonometry Questions

Trick 1 — Standard Angle Memory Trick

0°, 30°, 45°, 60°, 90°

sin values pattern:

√0 / 2
√1 / 2
√2 / 2
√3 / 2
√4 / 2

Trick 2 — Complementary Angle Rule

sin (90° − θ) = cos θ
cos (90° − θ) = sin θ
tan (90° − θ) = cot θ

Trick 3 — Identity Shortcut

If expression contains:

sin²θ + cos²θ

Direct answer:

15 High-Level Important MCQs with Answers and Step-by-Step Solutions in Trigonometry for CUET UG GAT

Q 4482) If $sin θ = 5 3$ , find $cos θ$ .

A. 4/5
B. 3/5
C. 5/4
D. 1/5

Answer:

A. 4/5

Step-by-Step Solution:

Using identity:

$sin^{2} θ + cos^{2} θ = 1$ $(53)^{2} + cos^{2} θ = 1$ $259 + cos^{2} θ = 1$ $cos^{2} θ = 2516$ $cos θ = 54$

Q 4483) Find the value of:

$tan 4 5^{\circ} + cos 6 0^{\circ}$

A. 1
B. 3/2
C. 2
D. 1/2

Answer:

B. 3/2

Solution:

$tan 4 5^{\circ} = 1, cos 6 0^{\circ} = 21$ $1 + 21 = 23$

Q 4484) Evaluate:

$sin 3 0^{\circ} + cos 0^{\circ}$

A. 1
B. 3/2
C. 1/2
D. 2

Answer:

B. 3/2

Solution:

$sin 3 0^{\circ} = 21, cos 0^{\circ} = 1$ $21 + 1 = 23$

Q 4485) Simplify:

$cos ^{2} θ 1 - sin ^{2} θ$

A. 1
B. sec²θ
C. tan²θ
D. cot²θ

Answer:

A. 1

Solution:

$1 - sin^{2} θ = cos^{2} θ$ $cos ^{2} θ cos ^{2} θ = 1$

Q 4486) Find the value of:

$sin 6 0^{\circ} \times cos 3 0^{\circ}$

A. 1/2
B. 3/4
C. √3/2
D. 1

Answer:

B. 3/4

Solution:

$sin 6 0^{\circ} = 2 3, cos 3 0^{\circ} = 2 3$ $2 3 \times 2 3 = 43$

Q 4487) Evaluate:

$tan 0^{\circ} + sin 9 0^{\circ}$

A. 1
B. 0
C. 2
D. Undefined

Answer:

A. 1

Solution:

$tan 0^{\circ} = 0, sin 9 0^{\circ} = 1$ $0 + 1 = 1$

Q 4488)Find value of:

$cos θ sin θ$

A. cot θ
B. tan θ
C. sec θ
D. cosec θ

Answer:

B. tan θ

Solution:

$tan θ = cos θ sin θ$

Q 4489) Simplify:

$1 + tan^{2} θ$

A. sin²θ
B. sec²θ
C. cos²θ
D. cot²θ

Answer:

B. sec²θ

Q 4490) Evaluate:

$cos 9 0^{\circ} - sin 0^{\circ}$

A. 1
B. 0
C. -1
D. 2

Answer:

B. 0

Solution:

$cos 9 0^{\circ} = 0, sin 0^{\circ} = 0$ $0 - 0 = 0$

Q 4491) If $tan θ = 12 5$ , find $sin θ$ .

A. 5/13
B. 12/13
C. 13/5
D. 12/5

Answer:

A. 5/13

Solution:

Use triangle:

Opp = 5, Adj = 12
Hyp = √(5² + 12²) = 13

$sin θ = 135$

Q 4492) Evaluate:

$sec 6 0^{\circ}$

A. 2
B. 1
C. √3
D. 1/2

Answer:

A. 2

Q 4493) Find:

$cot 4 5^{\circ}$

A. 1
B. 0
C. √3
D. 2

Answer:

A. 1

Q 4494) Evaluate:

$sin^{2} 3 0^{\circ} + cos^{2} 3 0^{\circ}$

A. 1
B. 1/2
C. 2
D. 0

Answer:

A. 1

Q 4495) Find value of:

$tan 6 0^{\circ}$

A. √3
B. 1
C. 0
D. 2

Answer:

A. √3

Q 4496) Evaluate:

$sin 30 ^{\circ} 1$

A. 1
B. 2
C. 1/2
D. √3

Answer:

B. 2

Important Observations from PYQs

1. Most Asked Topics

Standard angle values
Identities
Ratio conversions
Simple simplification

2. Difficulty Level

Easy to Moderate
Mostly formula-based

3. Strategy to Solve PYQs

Memorize standard values
Learn identities properly
Use triangle method for tan-based questions
Avoid lengthy calculations

Quick Revision Table (Must Remember)

Angle	sin	cos	tan
0°	0	1	0
30°	1/2	√3/2	1/√3
45°	1/√2	1/√2	1
60°	√3/2	1/2	√3
90°	1	0	∞

Frequently Asked Questions (FAQs)

Q1 — Is Trigonometry important for CUET UG GAT 2026?

Yes. Trigonometry is a frequently asked and scoring topic in the quantitative aptitude section of CUET.

Q2 — How many questions come from Trigonometry in CUET UG GAT?

Usually:

1 to 2 questions

Q3 — What are the most important topics in Trigonometry for CUET UG GAT?

Important topics include:

Trigonometric ratios
Identities
Standard angles
Complementary angles
Simplification

Q4 — Is Trigonometry easy to score in CUET?

Yes. With formula memorization and practice, it becomes one of the easiest scoring topics.

Conclusion – Trigonometry for CUET UG GAT

Trigonometry is one of the most important and scoring topics in the mathematics section of CUET UG GAT. Most questions are based on standard angle values, trigonometric identities, and simple applications, which makes this topic highly predictable and easy to master with regular practice. By learning key formulas, understanding identities, and solving previous year questions, students can improve both accuracy and speed in the exam.

Consistent revision of trigonometric concepts not only helps in solving direct questions but also builds a strong foundation for advanced topics like geometry, mensuration, and algebra. Therefore, dedicating sufficient time to practice Trigonometry can significantly boost overall performance and help students secure higher marks in the CUET examination.

Final Tip:
Focus on memorizing standard values, practice daily MCQs, and revise formulas regularly to score full marks in Trigonometry in CUET UG GAT 2026.

Internal Links

Trigonometry for CUET UG GAT

Mensuration for CUET GAT 2026

Probability for CUET GAT 2026

Introduction to Trigonometry

What is Trigonometry?

Basic Trigonometric Ratios

Important Trigonometric Identities

Why Trigonometry is Important for CUET UG GAT 2026?

Common Patterns of Questions in Trigonometry for CUET UG GAT

Short Tricks to Solve Trigonometry Questions

Trick 1 — Standard Angle Memory Trick

Trick 2 — Complementary Angle Rule

Trick 3 — Identity Shortcut

15 High-Level Important MCQs with Answers and Step-by-Step Solutions in Trigonometry for CUET UG GAT

Q 4482) If sin⁡θ=35sinθ=53​, find cos⁡θcosθ.

Answer:

Step-by-Step Solution:

Q 4483) Find the value of:

tan⁡45∘+cos⁡60∘tan45∘+cos60∘

Answer:

Solution:

Q 4484) Evaluate:

sin⁡30∘+cos⁡0∘sin30∘+cos0∘

Answer:

Solution:

Q 4485) Simplify:

1−sin⁡2θcos⁡2θcos2θ1−sin2θ​

Answer:

Solution:

Q 4486) Find the value of:

sin⁡60∘×cos⁡30∘sin60∘×cos30∘

Answer:

Solution:

Q 4487) Evaluate:

tan⁡0∘+sin⁡90∘tan0∘+sin90∘

Answer:

Solution:

Q 4488)Find value of:

sin⁡θcos⁡θcosθsinθ​

Answer:

Solution:

Q 4489) Simplify:

1+tan⁡2θ1+tan2θ

Answer:

Q 4490) Evaluate:

cos⁡90∘−sin⁡0∘cos90∘−sin0∘

Answer:

Solution:

Q 4491) If tan⁡θ=512tanθ=125​, find sin⁡θsinθ.

Answer:

Solution:

Q 4492) Evaluate:

sec⁡60∘sec60∘

Answer:

Q 4493) Find:

cot⁡45∘cot45∘

Answer:

Q 4494) Evaluate:

sin⁡230∘+cos⁡230∘sin230∘+cos230∘

Answer:

Q 4495) Find value of:

tan⁡60∘tan60∘

Answer:

Q 4496) Evaluate:

1sin⁡30∘sin30∘1​

Answer:

Important Observations from PYQs

1. Most Asked Topics

2. Difficulty Level

3. Strategy to Solve PYQs

Quick Revision Table (Must Remember)

Frequently Asked Questions (FAQs)

Q1 — Is Trigonometry important for CUET UG GAT 2026?

Yes. Trigonometry is a frequently asked and scoring topic in the quantitative aptitude section of CUET.

Q2 — How many questions come from Trigonometry in CUET UG GAT?

Q3 — What are the most important topics in Trigonometry for CUET UG GAT?

Q4 — Is Trigonometry easy to score in CUET?

Conclusion – Trigonometry for CUET UG GAT

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Authored and published by Vimal Kumar Tulsyan

Organisation: CUET NOW

Q 4482) If $sin θ = 5 3$ , find $cos θ$ .

$tan 4 5^{\circ} + cos 6 0^{\circ}$

$sin 3 0^{\circ} + cos 0^{\circ}$

$cos ^{2} θ 1 - sin ^{2} θ$

$sin 6 0^{\circ} \times cos 3 0^{\circ}$

$tan 0^{\circ} + sin 9 0^{\circ}$

$cos θ sin θ$

$1 + tan^{2} θ$

$cos 9 0^{\circ} - sin 0^{\circ}$

Q 4491) If $tan θ = 12 5$ , find $sin θ$ .

$sec 6 0^{\circ}$

$cot 4 5^{\circ}$

$sin^{2} 3 0^{\circ} + cos^{2} 3 0^{\circ}$

$tan 6 0^{\circ}$

$sin 30 ^{\circ} 1$