Trigonometry Most Expected Questions for SSC CGL Tier 2 Exam

Trigonometry for SSC CGL Tier 2 Exam

Trigonometry for SSC CGL Exam: The Staff Selection Commission (SSC) conducts the SSC CGL exam every year. As per the selection process of 2024, the SSC has successfully conducted the SSC CGL Tier 1 exam. As the next step, the SSC will conduct the SSC CGL Tier 2 exam. Passing the Tier 2 exam is not an easy task. For the best preparation for the exam, candidates must prepare topic-wise to get a deep insight into the exam. In this blog, we have provided a basic concept about the trigonometry and most expected questions that can be asked in the SSC CGL Tier 2 exam. Trigonometry is a topic that belongs to the Quantitative Aptitude section in the Tier 2 exam. Candidates can expect at least 5-9 questions from this topic in the SSC CGL Tier 2 exam. Candidates who are going to appear in the exam must go through this blog carefully.

Concept of Trigonometry

Definition:

Trigonometry is a topic of quantitative aptitude that deals with the relationships between the angles and sides of triangles, particularly right-angled triangles. The fundamental concept in trigonometry revolves around the ratios of the sides of a right-angled triangle relative to its angles.

Basic Trigonometric Ratios:

In a right-angled triangle, let:

• θ be one of the non-right angles,
• Opposite be the side opposite to the angle θ,
• Adjacent be the side adjacent to the angle θ,
• Hypotenuse be the side opposite the right angle (the longest side).

The six fundamental trigonometric ratios are defined as:

1. Sine (sin⁡):

2. Cosine (cos⁡):

3. Tangent (tan⁡):

4. Cosecant (csc⁡): (Reciprocal of sine)

5. Secant (sec⁡): (Reciprocal of cosine)

6. Cotangent (cot⁡): (Reciprocal of tangent)

Pythagorean Theorem:

For a right-angled triangle, the relationship between the sides is given by:

Hypotenuse²=Opposite²+Adjacent²

This is a fundamental relationship used to derive many trigonometric identities.

Trigonometric Identities:

1. Pythagorean Identities:

2. Reciprocal Identities:

3. Quotient Identities:

4. Co-function Identities:

Angle Sum and Difference Identities:

1. Sine of sum and difference:

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

2. Cosine of sum and difference:

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

3. Tangent of sum and difference:

Double Angle and Half-Angle Formulas:

1. Sine Double Angle:

sin(2θ) = 2 sin(θ) cos(θ)

2. Cosine Double Angle:

cos(2θ) = cos²(θ)−sin²(θ)

or equivalently:

cos(2θ) = 2 cos²(θ) − 1
cos(2θ) = 1−2 sin²(θ)

3. Tangent Double Angle:

4. Half-Angle Formulas:

Law of Sines and Law of Cosines:

These laws are used in any triangle, not just right-angled ones.

1. Law of Sines:

where a,b,c are the sides of the triangle, and A,B,C are the opposite angles.

2. Law of Cosines:

This formula helps find a side of a triangle when two sides and the included angle are known, or it can be used to find angles when all three sides are known.

Trigonometric Functions of Any Angle:

For angles greater than 90°, the values of trigonometric functions can be determined using the unit circle. The unit circle approach defines each of the trigonometric functions for all real angles (not just those in a right triangle).

Most Expected Important Questions PDF for Trigonometry

Question 1: What is the minimum value of 4(sin⁴θ + cos⁴θ – 2sin²θcos²θ)?

A) 1

B) 0

C) -1

D) 4

Question 2: When the altitude of the sun changes from 30° to 45°, the length of the shadow of an electricity pole on level ground decreases by 20 cm. What is the height of the electricity pole?

A) 8(√3 – 1) cm

B) 10(√3 – 1) cm

C) 5(√5 + 1) cm

D) 10(√3 + 1) cm

Question 3: If 3(sin²θ + cos²θ) = 4cos²θ, 0° < θ < 90°, the value of (tan²θ + cos²θ + sec²θ) is:

A) (10/7)

B) (15/19)

C) (29/12)

D) (30/13)

Question 4: The difference between the height of a pole and the length of its shadow is 4(√3 – 1) cm. If the height of the pole is 4√3 cm, then find the angle of elevation of the sun.

A) 60°

B) 45°

C) 30°

D) 90°

Question 5: The value of [sec(70°+ θ) – cosec(20°- θ) – cos²64° – cos²26°]/(sin32°cos58° + cos32°sin58°) is:

A) 0

B) -1

C) 1

D) 2

SSC CGL 2024 Tier 2 Free Preparation Resources

Below we are providing the SSC CGL 2024 Tier 2 Free Preparation Resources that contains multiple tests, including section-wise mock tests covering all the sections like English, General Awareness, Quantitative Aptitude, and Reasoning. Practicing these tests will help you revise all these sections in a time-bound manner and also test your skills and knowledge acquired in the last stretch of revision.

SSC CGL 2024 Tier 2 Free Preparation Resources
Task 1	SSC CGL 2024 Tier 2 Free Mock Test	Mini Mock Tests
Task 2	Quantitative Aptitude Free Mock Tests	Sectional Mock Tests
Task 3	English Free Mock Tests	Previous Year Question Paper
Task 4	General Awareness Free Mock Tests	Mock Test 1
Task 5	Reasoning Free Mock Tests	Mock Test 2

Other Blogs of SSC CGL 2024
SSC CGL Exam Pattern	SSC CGL Syllabus
SSC CGL Study Plan	SSC CGL Selection Process
SSC CGL Cut Off	SSC CGL Preparation Strategy
SSC CGL Previous Year Question Papers

Trigonometry Most Expected Questions for SSC CGL Tier 2 Exam FAQs