TRIGONOMETRIC IDENTITIES

Where it occurs below,t = tan ½ A

Sin (180°-Ɵ°) = sin Ɵ°
Sin (180°+Ɵ°) = - sin Ɵ°
Sin (360-Ɵ)° =-sinƟ°
Sin A = 2t/1+t²
sin²A + cos²A = 1
Sin 2A = 2sinAcosA
Sin (A± B) = sinAcosB±cosAsinB
Sin A + Sin B = 2sin⅟₂(A+B)cos⅟₂(A-B)
Sin A – Sin B = 2cos⅟₂(A+B)sin⅟₂(A-B)
2 sin A sin B = cos (A-B)cos(A+B)
Cos (180-Ɵ)° = -cosƟ°
Cos (180+Ɵ)° = -cosƟ°
Cos (360-Ɵ)° = cos Ɵ°
Sin (90-Ɵ)° = cos Ɵ°
Sin (-Ɵ)° = -sin Ɵ°
Cos (90-Ɵ)° = -tan Ɵ°
Cos (-0) = cos Ɵ°
Tan (90-Ɵ)° = -tan Ɵ°

Where t = tan cos (A±B) = cos A cos B ±sin⁡〖A sin⁡B 〗
Cos A + Cos B = 2cos⅟₂(A+B)cos⅟₂(A-B)
Cos A- Cos B = -2sin⅟₂ (A+B) sin⅟₂ (A-B)
2 cos AcosB = cos (A+B)+cos(A-B)






1 + cos 2A = 2 cos²A
1 – cos 2A = 2 sin²A
Tan (180-Ɵ)° = -tan Ɵ°
Tan (180+Ɵ)° = tan Ɵ°
Tan (360-Ɵ)° = -tan Ɵ°
Tan A = 2t/1-t²
Tan 2A = 2tan A/1-tan²A
Tan (A± B) = tanA ± tanB / 1 ∓ tanAtanB
1 + tan²A = sec²A
1 + cot²A = cosec²A