Compound Angles — Addition formulas
Trigonometric Functions & Equations
8
JEE Qs
8%
Hard
75
min
Mastering the compound angle formulas and their reverse application is fundamental for almost all advanced trigonometry topics, so prioritize deep understanding and quick recall.
🧮 Key Formulas
✅ Key Points for JEE
- 1Memorize all addition/subtraction formulas for sin, cos, tan, and cot thoroughly for quick recall and error-free application.
- 2Be proficient in applying these formulas in reverse to simplify expressions, e.g., recognizing 'sin A cos B + cos A sin B' as 'sin(A+B)'.
- 3Practice calculating exact trigonometric values for angles like 15°, 75°, 105°, etc., by expressing them as sums or differences of standard angles (e.g., 45° ± 30°).
- 4Understand the conditions under which tan(A±B) and cot(A±B) formulas are valid (denominators not zero), especially when dealing with general solutions.
⚠️ Common Mistakes
- ✕Incorrectly using signs in formulas, particularly for cos(A+B) and tan(A-B).
- ✕Mistaking sin(A+B) for sin A + sin B (and similar errors for other functions), which is a fundamental misconception.
- ✕Errors in algebraic manipulation while simplifying complex trigonometric expressions involving compound angles.
- ✕Forgetting to check the domain conditions for tan and cot functions (e.g., A, B, A±B not being odd multiples of π/2 for tan).
📝 Practice Questions
See allQ11.Let the range of the function f(x) = 6 + 16 cos x ⋅cos ( π3 −x) ⋅cos ( π3 + x) ⋅sin 3x ⋅cos 6x, x ∈R be [α, β] . Then the distance of the point (α, β) from the line 3x + 4y + 12 = 0 is : (1) 11 (2) 8 (3) 10 (4) 9 sin y > 0 and x(1) = π2 . Then
Q7. If ∑13r=1 { sin( 4 +(r−1) 6 ) sin( π4 + rπ6 ) } (1) 10 (2) 4 (3) 2 (4) 8
Q18.The sum of all values of θ ∈[0, 2π] satisfying 2 sin2 θ = cos 2θ and 2 cos2 θ = 3 sin θ is 2025 (22 Jan Shift 2) JEE Main Previous Year Paper (1) 4π (2) 5π6 (3) π (4) π 2
Q18.The value of (sin 70∘) (cot 10∘cot 70∘−1) is (1) 2/3 (2) 1 (3) 0 (4) 3/2 dx 1 1 1 , then 3( b + c) is equal to
Q22.If for some α, β; α ≤β, α + β −8 and sec2 (tan−1 α) + cosec2 (cot−1 β) −36, then α2 + β is_______. Q23. ⎡x⎤ Let A be a 3 × 3 matrix such that X TAX = O for all nonzero 3 × 1 matrices X = y . If ⎣z ⎦ ⎡ 1 ⎤ ⎡ 1 ⎤ ⎡1 ⎤ ⎡ 0 ⎤ A 1 = 4 , A 2 = 4 , and det(adj(2(A + 1))) −2α3β5γ, α, β, γ ∈N , then α2 + β2 + γ 2 ⎣ 1⎦ ⎣ −5 ⎦ ⎣1⎦ ⎣−8 ⎦ is_____. x ≥0. Then
Q20.If sin x + sin2 x = 1, x ∈(0, π2 ), then (cos12 x + tan12 x) + 3 (cos10 x + tan10 x + cos8 x + tan8 x) + (cos6 x + tan6 x) is equal to : (1) 4 (2) 1 (3) 3 (4) 2 π
NCERT Chapters
- Class 11 Mathematics Ch 3: Trigonometric Functions