Trigonometry Formulas For Class 10 - Basic Trigonometric Formulas, Identities & Angle Formulas

Oct 13, 2026

Trigonometry Formulas For Class 10 compiles essential trigonometric ratios and their mathematical meaning, including sin, cos, tan, cot, cosec, and sec. It explains reciprocal relations between trigonometric functions, sign functions for −θ across all major functions, and foundational identities such as sin²A + cos²A = 1. It further covers periodic identities, complementary ratios by quadrant, and sum, difference, double-angle, and triple-angle formulas for sin, cos, and tan.

LanguageEnglish

CategoryForms

FormatPDF

Pages4

Reading Time2 min

AccessFree to download

Basic Trigonometric formulas

Trigonometric ratios

Reciprocal relations between trigonometric ratios

Trigonometric sign functions

Trigonometric identities and periodic identities

Complementary ratios by quadrant

Sum and difference of two angles

Double angle formulas

Triple angle formulas

Trigonometry Formulas For Class 10 Basic Trigonometric formulas | [S.no](S.no) | Trigonometric ratios | Mathematical value | | --- | --- | --- | | 1 | sinA | Perpendicular/Hypotenuse | | 2 | cos A | Base/Hypotenuse | | 3 | tanA | Perpendicular/Base | | --- | --- | --- | | 4 | cotA | Base/Perpendicular | | 5 | cosec A | Hypotenuse/Perpendicular | | 6 | sec A | Hypotenuse/Base | |
Reciprocal Relation Between Trigonometric Ratios | | | | --- | --- | --- | | [S.no](S.no) | Trigonometric ratios | Relation | | 1 | tanA | sinA/cosA | | 2 | cotA | cos A/sinA | | 3 | cosec A | 1/sin A | | 4 | sec A | 1/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 = sec 2A 3. cot2A + 1 = cosec 2A 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) = sinA cos B + cos A sin B ● sin (A − B) = sinA cos B – cos A sin B ● cos (A + B) = cos A cos B – sinA sin B ● cos (A– B) = cos A cos B + sinA 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 ● sin 2A = 2 sin A cos A = [2 tan A /(1 + tan 2A)] ● cos 2A = cos 2A– sin2A = 1 – 2 sin 2A = 2 cos 2A– 1= [(1-tan2A)/(1 + tan2A)] ● tan 2A = (2 tan A)/(1-tan 2A) Triple Angle Formulas ● sin 3A = 3 sinA– 4 sin 3A ● cos 3A = 4 cos 3A– 3cosA ● tan 3A = [3 tanA– tan3A]/[1 − 3 tan2A]

FAQs

What are the basic trigonometric ratios for Class 10?

The document lists sinA, cosA, tanA, cotA, cosecA, and secA, along with their corresponding geometric interpretations (perpendicular/base/hypotenuse relationships).

What reciprocal relations connect the trigonometric ratios?

It provides tanA = sinA/cosA, cotA = cosA/sinA, cosecA = 1/sinA, and secA = 1/cosA.

Which angle formulas are included for solving trig problems?

It includes identities for sum and difference of two angles, double-angle formulas, and triple-angle formulas for sin, cos, and tan.

Oct 13, 2026

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