Compound angle values: Class 11 practice

What you should know first

• Standard trigonometric values

The idea behind compound angle values

sin(A ± B) = sinA cosB ± cosA sinB, cos(A ± B) = cosA cosB ∓ sinA sinB. Writing angles like 75° or 15° as sums/differences of 30°, 45°, 60° gives exact values.

Step-by-step method

1. Write the angle as a sum or difference of standard angles.
2. Apply the formula.
3. Substitute exact values and simplify.

Worked example 1 (Basic)

Find the exact value of sin 285°.

1. Write as sin(240° + 45°)
2. Apply the formula
3. = −(√6 + √2)/4
4. Answer: −(√6 + √2)/4

Worked example 2 (Standard)

Find the exact value of cos 165°.

1. Write as cos(120° + 45°)
2. Apply the formula
3. = −(√6 + √2)/4
4. Answer: −(√6 + √2)/4

Worked example 3 (Challenge)

Find the exact value of sin 165°.

1. Write as sin(120° + 45°)
2. Apply the formula
3. = (√6 − √2)/4
4. Answer: (√6 − √2)/4

Common mistakes and misconceptions

• sin(A + B) = sin A + sin B
• Sign errors in cos(A + B)

Practice questions

1. (Basic) Find the exact value of tan 15°.
2. (Basic) Find the exact value of cos 105°.
3. (Standard) Find the exact value of cos 15°.
4. (Standard) Find the exact value of tan 75°.
5. (Challenge) Find the exact value of sin 15°.
6. (Challenge) Find the exact value of sin 105°.

Answer key with full working

• Q1: Write as tan(45° − 30°) → Apply the formula → = 2 − √3 → Answer: 2 − √3
• Q2: Write as cos(60° + 45°) → Apply the formula → = (√2 − √6)/4 → Answer: (√2 − √6)/4
• Q3: Write as cos(45° − 30°) → Apply the formula → = (√6 + √2)/4 → Answer: (√6 + √2)/4
• Q4: Write as tan(45° + 30°) → Apply the formula → = 2 + √3 → Answer: 2 + √3
• Q5: Write as sin(45° − 30°) → Apply the formula → = (√6 − √2)/4 → Answer: (√6 − √2)/4
• Q6: Write as sin(60° + 45°) → Apply the formula → = (√6 + √2)/4 → Answer: (√6 + √2)/4

Syllabus note

This skill is listed under "Trigonometric Functions" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

Related practice and notes

• Trigonometric Functions chapter notes (Class 11)
• Radians, degrees and arc length
• General solutions of trigonometric equations
• Permutations and combinations problems
• Binomial theorem: general term and coefficients
• Counting with Venn diagrams
• Domain and range of functions
• All Class 11 practice

Frequently asked questions

Which chapter is compound angle values in?

"Trigonometric Functions", Class 11 Maths (NCERT/CBSE). Other boards may place it differently.

How were the answers checked?

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.