JEEClass 11-12
Trigonometry Formulas for JEE
Every trigonometry formula you need for JEE Main and Advanced, organized by category. Bookmark this page for quick revision.
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Basic Identities
Pythagoreansin²θ + cos²θ = 1
Pythagorean (tan)1 + tan²θ = sec²θ
Pythagorean (cot)1 + cot²θ = csc²θ
Reciprocalsinθ = 1/cscθ, cosθ = 1/secθ, tanθ = 1/cotθ
Quotienttanθ = sinθ/cosθ, cotθ = cosθ/sinθ
Compound Angle Formulas
sin(A+B)sin(A+B) = sinAcosB + cosAsinB
sin(A−B)sin(A−B) = sinAcosB − cosAsinB
cos(A+B)cos(A+B) = cosAcosB − sinAsinB
cos(A−B)cos(A−B) = cosAcosB + sinAsinB
tan(A+B)tan(A+B) = (tanA + tanB) / (1 − tanAtanB)
tan(A−B)tan(A−B) = (tanA − tanB) / (1 + tanAtanB)
Double Angle Formulas
sin2Asin2A = 2sinAcosA
cos2A (form 1)cos2A = cos²A − sin²A
cos2A (form 2)cos2A = 2cos²A − 1
cos2A (form 3)cos2A = 1 − 2sin²A
tan2Atan2A = 2tanA / (1 − tan²A)
Half angle (sin)sin²(A/2) = (1 − cosA) / 2
Half angle (cos)cos²(A/2) = (1 + cosA) / 2
Triple Angle Formulas
sin3Asin3A = 3sinA − 4sin³A
cos3Acos3A = 4cos³A − 3cosA
tan3Atan3A = (3tanA − tan³A) / (1 − 3tan²A)
Product-to-Sum
sinAcosB2sinAcosB = sin(A+B) + sin(A−B)
cosAsinB2cosAsinB = sin(A+B) − sin(A−B)
cosAcosB2cosAcosB = cos(A+B) + cos(A−B)
sinAsinB2sinAsinB = cos(A−B) − cos(A+B)
Sum-to-Product
sinC + sinDsinC + sinD = 2sin((C+D)/2)cos((C−D)/2)
sinC − sinDsinC − sinD = 2cos((C+D)/2)sin((C−D)/2)
cosC + cosDcosC + cosD = 2cos((C+D)/2)cos((C−D)/2)
cosC − cosDcosC − cosD = −2sin((C+D)/2)sin((C−D)/2)
General Solutions
sinθ = sinαθ = nπ + (−1)ⁿα, n ∈ ℤ
cosθ = cosαθ = 2nπ ± α, n ∈ ℤ
tanθ = tanαθ = nπ + α, n ∈ ℤ
Inverse Trigonometric Functions
sin⁻¹x rangesin⁻¹x ∈ [−π/2, π/2], x ∈ [−1, 1]
cos⁻¹x rangecos⁻¹x ∈ [0, π], x ∈ [−1, 1]
tan⁻¹x rangetan⁻¹x ∈ (−π/2, π/2), x ∈ ℝ
tan⁻¹x + tan⁻¹ytan⁻¹x + tan⁻¹y = tan⁻¹((x+y)/(1−xy)), xy < 1
sin⁻¹x + cos⁻¹xsin⁻¹x + cos⁻¹x = π/2
JEE Tips
- Tip 1:Compound angle formulas are the most tested — derive double and triple angle from them
- Tip 2:For JEE, memorize product-to-sum and sum-to-product — they simplify integration problems
- Tip 3:Always check the principal value range before solving inverse trig equations