S N Dey Mathematics Class 11 Trigonometry solutions explained chapter-wise with fully worked examples for every formula type. WBCHSE-ready.

S N Dey Mathematics Class 11 Trigonometry Solutions: The Complete Chapter-Wise Worked Guide

If you’ve searched “S N Dey Mathematics Class 11 Trigonometry solutions,” you’re probably staring at compound angle formulas, multiple angle identities, or a trigonometric equation that refuses to simplify — and you need more than just a final answer. You need to see how it’s solved.

That’s exactly what this guide gives you. S. N. Dey’s Class 11 Mathematics is one of the most widely used textbooks for WBCHSE (West Bengal Council of Higher Secondary Education) students, and its Trigonometry section — spread across several interconnected chapters — forms the backbone of everything you’ll study later in Class 12, and in competitive exams like WBJEE.

Below, you’ll find a chapter-wise map of the trigonometry syllabus as covered in S. N. Dey, plus a fully worked solution for a representative problem from each chapter, so you can apply the same method to your own textbook exercises with confidence.

Why S N Dey’s Trigonometry Section Matters So Much

Unlike a single standalone chapter, trigonometry in S. N. Dey is built in layers — each chapter depends on the one before it:

• Standard angles and trigonometric functions lay the foundation
• Compound angles extend that foundation to sums and differences of angles
• Multiple and submultiple angles are derived directly from compound angle formulas
• Transformation formulas convert between sums/differences and products
• Trigonometric equations apply all of the above to solve for unknown angles
• Properties of triangles apply trigonometric ratios to real triangle geometry

Miss one link in this chain, and everything after it becomes noticeably harder — which is exactly why solving each chapter properly (not just memorising identities) pays off for the rest of the syllabus.

Chapter-Wise Breakdown of S N Dey Trigonometry

Chapter	Core Focus	Key Formulas You’ll Use
Trigonometric Functions & Standard Angles	Signs, ranges, and values at standard angles	ASTC rule, values at 0°, 30°, 45°, 60°, 90°
Trigonometric Functions of Compound Angles	Sum and difference of two angles	sin(A±B), cos(A±B), tan(A±B)
Trigonometric Functions of Multiple Angles	Expressing 2A, 3A in terms of A	sin 2A, cos 2A, tan 2A, sin 3A, cos 3A
Trigonometric Functions of Submultiple Angles	Expressing A in terms of A/2	sin A, cos A, tan A using half-angle
Transformation Formulas	Sum-to-product and product-to-sum	sin C + sin D, cos C − cos D, etc.
General Solutions of Trigonometric Equations	Solving for all possible angle values	General solution forms for sin θ, cos θ, tan θ
Properties of Triangles	Relating sides and angles of a triangle	Sine rule, cosine rule, projection formula

Detailed Worked Solutions – One Per Chapter

1. Trigonometric Functions and Standard Angles

Sample problem: Find the value of sin 150° + cos 240°.

Solution: sin 150° = sin(180° − 30°) = sin 30° = 1/2 cos 240° = cos(180° + 60°) = −cos 60° = −1/2

sin 150° + cos 240° = 1/2 + (−1/2) = 0

Method to remember: Reduce every non-standard angle to its nearest multiple of 90° or 180°, apply the correct sign using the ASTC rule (All positive in Q1, Sin positive in Q2, Tan positive in Q3, Cos positive in Q4), and only then substitute the standard value.

2. Trigonometric Functions of Compound Angles

Sample problem: Find the value of sin 75° using the compound angle formula.

Solution: Write 75° = 45° + 30°

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

sin 75° = sin 45° cos 30° + cos 45° sin 30° = (√2/2)(√3/2) + (√2/2)(1/2) = (√6/4) + (√2/4) = (√6 + √2) / 4

Method to remember: Always split the given angle into two standard angles whose sine and cosine you already know, then apply the correct compound angle identity directly — don’t try to memorise values for non-standard angles separately.

3. Trigonometric Functions of Multiple Angles

Sample problem: If sin θ = 3/5 and θ is acute, find the value of sin 2θ.

Solution: Since θ is acute and sin θ = 3/5, using sin²θ + cos²θ = 1: cos²θ = 1 − 9/25 = 16/25 cos θ = 4/5 (positive, since θ is acute)

sin 2θ = 2 sin θ cos θ sin 2θ = 2 × (3/5) × (4/5) = 24/25

Method to remember: Multiple angle problems almost always require finding the missing ratio (sin, cos, or tan) first using the Pythagorean identity, before substituting into the double or triple angle formula.

4. Trigonometric Functions of Submultiple Angles

Sample problem: If cos A = 7/25 and A lies between 0° and 90°, find sin(A/2).

Solution: Using cos A = 1 − 2sin²(A/2): 7/25 = 1 − 2sin²(A/2) 2sin²(A/2) = 1 − 7/25 = 18/25 sin²(A/2) = 9/25 sin(A/2) = 3/5 (positive, since A/2 lies between 0° and 45°)

Method to remember: Choose the half-angle formula that directly matches the given ratio (cos A in terms of sin(A/2), or in terms of cos(A/2)) so you avoid unnecessary extra steps.

5. Transformation Formulas

Sample problem: Express sin 5x + sin 3x as a product.

Solution: Using sin C + sin D = 2 sin[(C+D)/2] cos[(C−D)/2]

sin 5x + sin 3x = 2 sin[(5x+3x)/2] cos[(5x−3x)/2] = 2 sin(4x) cos(x)

Answer: 2 sin 4x cos x

Method to remember: Identify whether you’re converting a sum/difference to a product (transformation formula) or the reverse — the formula you need depends entirely on which direction the question is asking you to go.

6. General Solutions of Trigonometric Equations

Sample problem: Solve sin θ = 1/2 for the general solution.

Solution: We know sin 30° = 1/2, so the principal value is θ = 30° = π/6

The general solution for sin θ = sin α is: θ = nπ + (−1)ⁿ α, where n is any integer

θ = nπ + (−1)ⁿ (π/6), n ∈ ℤ

Method to remember: First identify the principal value using a known standard angle, then apply the correct general solution template based on whether the equation involves sin, cos, or tan — each has its own distinct formula.

7. Properties of Triangles

Sample problem: In triangle ABC, if a = 7, b = 8, and angle C = 60°, find side c using the cosine rule.

Solution: Cosine rule: c² = a² + b² − 2ab cos C

c² = 7² + 8² − 2(7)(8) cos 60° c² = 49 + 64 − 112 × (1/2) c² = 113 − 56 c² = 57

c = √57 ≈ 7.55

Method to remember: Use the cosine rule when you know two sides and the included angle; switch to the sine rule when you know a side and its opposite angle along with one more angle or side.

The 4-Step Method to Apply This to Your Own Textbook Exercises

1. Identify which chapter’s formula the question is testing using the table above.
2. Match your problem’s structure to the closest worked example — same formula type, same setup.
3. Substitute your own given values, being careful with signs and quadrant rules.
4. Simplify step-by-step, and sanity-check the final answer’s range (e.g., sine and cosine values must always lie between −1 and 1).

Common Mistakes That Cost Marks in Trigonometry

• Ignoring the quadrant/sign rule when reducing non-standard angles.
• Applying the wrong half-angle formula — always match it to the given ratio.
• Forgetting the “+2nπ” or general solution structure entirely, and giving only the principal value.
• Mixing up sine rule and cosine rule conditions — check what’s given (sides vs. angles) before choosing.
• Skipping the Pythagorean identity step in multiple angle problems, leading to an incomplete or wrong substitution.

Where to Verify Your Answers the Right Way

1. Your subject teacher or school study group — fastest and most reliable for exact wording expected in WBCHSE answers.
2. The worked examples inside your own copy of S. N. Dey, since most exercise problems are direct extensions of these.
3. Standard formula sheets for compound, multiple, and submultiple angle identities, to double-check your formula selection.
4. Cross-verification by substitution — plug your final angle or ratio back into the original equation wherever possible.

Copying complete worked solutions from unofficial scanned PDFs is risky: methods vary between solution sets, and WBCHSE examiners specifically award marks for the correct derivation steps — not just the final numeric answer.

Quick FAQ

Is S N Dey Class 11 Mathematics only for WBCHSE students? It’s primarily designed around the WBCHSE syllabus, though its clear step-by-step approach makes it a popular reference for other boards’ students too, especially for trigonometry fundamentals.

Which trigonometry chapter should I master first? Start with Standard Angles and Compound Angles — nearly every other chapter (multiple angles, submultiple angles, transformation formulas) is derived directly from these two.

Do I need to memorise every transformation formula separately? No. If you understand how sum-to-product and product-to-sum formulas are derived from the compound angle formulas, you can reconstruct any of them quickly instead of rote memorising six separate identities.

How important is Properties of Triangles for competitive exams like WBJEE? Very important — sine rule, cosine rule, and related triangle properties frequently appear in both board exams and competitive entrance tests, often combined with coordinate geometry or vectors.

Final Word

Trigonometry in S. N. Dey isn’t a chapter to memorise — it’s a chain of formulas where each one builds on the last. Work through the seven worked examples above, understand why each method was chosen (not just the final number), and apply the same reasoning to your own textbook exercises. That approach will serve you far better in your WBCHSE board exam — and in any competitive exam that follows — than any copied solution ever could.