**Trigonometric Identities and Formulas**

**There are three systems of measuring Angles-**

**1. Circular System**

- Unit of Measurement is radian.
- 180 degree = π radians

**2. Sexagesimal System (English System)**

- Right angle is divided into 90 equal parts called degree.
- Unit of Measurement is degree.
- Each degree is divided into 60 equal parts called minute. (1 degree = 60’)
- Each minute divided into 60 equal parts called seconds (1 minute = 60’’)

**3. Centesimal or French System**

- Right angle is divided into 100 equal parts.
- Unit of measurement is grades.
- Each grade is divided into 100 equal parts called minute, and minutes into seconds.

**Sign Conventions**

- cos (90 – θ) = sinθ
- tan (90 – θ) = cotθ
- cosec (90 – θ) = secθ
- sec (90 – θ) = cosecθ
- cot (90 – θ) = tanθ

**Some Basic Formulas and Identities**

**Advanced Trigonometric Identities**

**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)**

**cot (A + B) = (cot A cot B – 1) / (cot A + cot B)**

**cot (A – B) = (cot A cot B + 1) / (cot B – cot A)**

**sin 2θ = 2sinθcosθ**

**2sin A sin B = cos (A – B) – cos (A + B)**

**2cos A cos B = cos (A + B) + cos (A – B)**

**2sin A cos B = sin (A + B) + sin (A – B)**

**2cos A sin B = sin (A + B) – sin (A – B)**

**sinC + sinD = 2sin[(C + D)/2] × cos[(C – D)/2]**

**sinC – sinD = 2cos[(C + D)/2] × sin[(C – D)/2]**

**cosC + cosD = 2cos[(C + D)/2]cos[(C – D)/2]**

**cosC – cosD = 2sin[(C + D)/2]cos[(D – C)/2]**

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