Trigonometry Formulas For Class 10

Trigonometry is the study of relationships between angles, lengths, and heights of triangles. It includes ratios, function, identities, formulas to solve problems based on it, especially for right-angled triangles. Applications of trigonometry are also found in engineering, astronomy, Physics and architectural design. This chapter is very important as it comprises many topics like Linear Algebra, Calculus and Statistics.

Trigonometry is introduced in CBSE Class 10. It is a completely new and tricky chapter where one needs to learn all the formula and apply them accordingly. Trigonometry Class 10 formulas are tabulated below.

List of Trigonometric Formulas for 10th

Trigonometry Formulas for Class 10

Applying Pythagoras theorem for the given right-angled triangle, we have:

(Perpendicular)2+(Base)2=(Hypotenuse)2

⇒(P)2+(B)2=(H)2

The Trigonometric formulas are given below:

S.noPropertyMathematical value
1sin APerpendicular/Hypotenuse
2cos ABase/Hypotenuse
3tan APerpendicular/Base
4cot ABase/Perpendicular
5cosec AHypotenuse/Perpendicular
6sec AHypotenuse/Base

Reciprocal Relation Between Trigonometric Ratios

S.noIdentityRelation
1tan Asin A/cos A
2cot Acos A/sin A
3cosec A1/sin A
4sec A1/cos A

Trigonometric Sign Functions

  • sin (-θ) = − sin θ
  • cos (−θ) = cos θ
  • tan (−θ) = − tan θ
  • cosec (−θ) = − cosec θ
  • sec (−θ) = sec θ
  • cot (−θ) = − cot θ

Trigonometric Identities

  1. sin2A + cos2A = 1
  2. tan2A + 1 = sec2A
  3. cot2A + 1 = cosec2A

Periodic Identities

  • sin(2nπ + θ ) = sin θ
  • cos(2nπ + θ ) = cos θ
  • tan(2nπ + θ ) = tan θ
  • cot(2nπ + θ ) = cot θ
  • sec(2nπ + θ ) = sec θ
  • cosec(2nπ + θ ) = cosec θ

Complementary Ratios

Quadrant I

  • sin(π/2−θ) = cos θ
  • cos(π/2−θ) = sin θ
  • tan(π/2−θ) = cot θ
  • cot(π/2−θ) = tan θ
  • sec(π/2−θ) = cosec θ
  • cosec(π/2−θ) = sec θ

Quadrant II

sin(π−θ) = sin θ
cos(π−θ) = -cos θ
tan(π−θ) = -tan θ
cot(π−θ) = – cot θ
sec(π−θ) = -sec θ
cosec(π−θ) = cosec θ

Quadrant III

  • sin(π+ θ) = – sin θ
  • cos(π+ θ) = – cos θ
  • tan(π+ θ) = tan θ
  • cot(π+ θ) = cot θ
  • sec(π+ θ) = -sec θ
  • cosec(π+ θ) = -cosec θ

Quadrant IV

  • sin(2π− θ) = – sin θ
  • cos(2π− θ) = cos θ
  • tan(2π− θ) = – tan θ
  • cot(2π− θ) = – cot θ
  • sec(2π− θ) = sec θ
  • cosec(2π− θ) = -cosec θ

Sum and Difference of Two Angles

  • sin (A + B) = sin A cos B + cos A sin B
  • sin (A − B) = sin A cos B – cos A sin B
  • cos (A + B) = cos A cos B – sin A sin B
  • cos (A – B) = cos A cos B + sin A sin B
  • tan(A+B) = [(tan A + tan B)/(1 – tan A tan B)]
  • tan(A-B) = [(tan A – tan B)/(1 + tan A tan B)]

Double Angle Formulas

  • sin2A = 2sinA cosA = [2tan A + (1+tan2A)]
  • cos2A = cos2A–sin2A = 1–2sin2A = 2cos2A–1= [(1-tan2A)/(1+tan2A)]
  • tan 2A = (2 tan A)/(1-tan2A)

Thrice of Angle Formulas

  • sin3A = 3sinA – 4sin3A
  • cos3A = 4cos3A – 3cosA
  • tan3A = [3tanA–tan3A]/[1−3tan2A]

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