SSC CHSL Trigonometry Questions, Basic Concepts, Free Test and PDF

If you’re an SSC CHSL 2025 aspirant, then you cannot skip the Trigonometry topic. It is one of the most important and scoring topics that belongs to the quantitative aptitude section of SSC CHSL exam. SSC can ask at least 2-3 questions from an easy to moderate level. To help you in scoring these marks, we have provided this blog. In this blog, we have provided SSC CHSL Trigonometry Questions with basic concepts, formulas, and other important things. To boost your preparation for SSC CHSL, you must take this blog seriously.

Trigonometry: Basic Concepts & Formulas

Trigonometry is the branch of mathematics dealing with the relationship between angles and sides of a triangle, especially right-angled triangles. It includes ratios, identities, and applications of trigonometric functions like sine, cosine, tangent, etc.

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:

Short Trick: If you see an expression like (1 – sin²θ) or (cosec²θ – cot²θ), immediately replace it with cos²θ and 1, respectively.

2. Reciprocal Identities:

3. Quotient Identities:

4. Co-function Identities:

Trick: Change the prefix to its “co-” counterpart. Sin becomes Cos, Tan becomes Cot, Sec becomes Cosec, and vice versa.

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 trigonometric function for all real angles (not just those in a right triangle).

Trigonometry Table

Below we have provided the trigonometry table for standard angles and some non-standard ones.

Trigonometry Table
θ	0° (0 radians)	30° (π/6)	45° (π/4)	60° (π/3)	90° (π/2)	180° (π)	270° (3π/2)	360° (2π)
sin	0	1/2	1/√2	√3/2	1	0	-1	0
cos	1	√3/2	1/√2	1/2	0	-1	0	1
tan	0	1/√3	1	√3	∞	0	∞	0
csc	∞	2	√2	2/√3	1	∞	-1	∞
sec	1	2/√3	√2	2	∞	-1	∞	1
cot	∞	√3	1	1/√3	0	∞	0	∞

SSC CHSL Trigonometry Questions, Download Free PDF

Here, we have provided the trigonometry questions for SSC CHSL exam. Before solving these questions, make sure to go through the formulas and concepts that we have provided above. After solving these questions, you will be able to determine the type of trigonometry questions asked in the SSC CHSL exam.

Q1. If X𝑠𝑖𝑛³𝜃 + 𝑦𝑐𝑜𝑠³𝜃 = 𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃, 𝑥𝑠𝑖𝑛𝜃 =𝑦𝑐𝑜𝑠𝜃, 𝑠𝑖𝑛𝜃 ≠ 0, 𝑐𝑜𝑠𝜃 ≠ 0, then x² + y² = ?

(a) 1/√2
(b) 1/2
(c) 1
(d) √2

Q2. If a(tanθ + cotθ)=1, sinθ + cosθ = b and 0 < θ < 90 then relation between a and b?

(a) b² = 2(a + 1)
(b) b² = 2(a – 1)
(c) 2a = b² – 1
(d) 2a = b² + 1

Q3. The value of:

(a) 1
(b) 2
(c) –1
(d) 0

Q4. If 𝑐𝑜𝑠𝜃 + 𝑠𝑖𝑛𝜃 = m, 𝑠𝑒𝑐𝜃 + 𝑐𝑜𝑠𝑒𝑐𝜃 = n then n(m² – 1) is equal to?

(a) 2m
(b) mn
(c) 4mn
(d) 2n

Q5. If A is an acute angle and cot A + cosec A = 3, then the value of sin A is

(a) 1
(b) 4/5
(c) 3/5
(d) 0

Q6. If A + B + C = π, then cos2A + cos2B + cos2C = ?

(a) 1 + 4 cosA cosB cosC
(b) –1 + 4 sinA sinB cosC
(c) –1 – 4 sinA cosB sinC
(d) 1 + 4 sinA sinb cosC

Q7. If A + B + C = 180º, then sin2A + sin2B + sin2C = ?

(a) 4 sinA sinB cosC
(b) 4 cosA cosB cosC
(c) 4 sinA sinB sinC
(d) 8 sinA sinB sinC

Q8. If tan A + sinA = p and tan A – sinA = q then which of the following is true?

(a) p² + q² = 4√pq
(b) p + q = pq
(c) p– q = pq
(d) p²– q² = 4√pq

Q9. If sin q + cos q = a and sec q + cosec q = b then

(a) a – b = b² –1
(b) a + b = 1
(c) 𝑎²– 1 = 2𝑎/𝑏
(d) 𝑎 =2𝑎/(𝑏²–1)

Q10. If cosec q – sin q =1 and sec q – cos q = m, then l² m²(l² + m² + 3) = ?

(a) 0
(b) 1
(c) –1
(d) 2

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