Trigonometry identities of maths | Trigo identities

Trigonometric Identities

The reciprocal trigonometric identities are:

Sin θ = 1/Csc θ or Csc θ = 1/Sin θ

Cos θ = 1/Sec θ or Sec θ = 1/Cos θ

Tan θ = 1/Cot θ or Cot θ = 1/Tan θ

Pythagorean Trigonometric Identities

sin2 a + cos2 a = 1

1+tan2 a = sec2 a

cosec2 a = 1 + cot2 a

Ratio Trigonometric Identities

The trigonometric ratio identities are:

Tan θ = Sin θ/Cos θ

Cot θ = Cos θ/Sin θ

Trigonometric Identities of Opposite Angles

The list of opposite angle trigonometric identities are:

Sin (-θ) = – Sin θ

Cos (-θ) = Cos θ

Tan (-θ) = – Tan θ

Cot (-θ) = – Cot θCot (-θ) = – Cot θ

Sec (-θ) = Sec θ

Csc (-θ) = -Csc θ

Trigonometric Identities of Complementary Angles

I

Sin (90 – θ) = Cos θ

Cos (90 – θ) = Sin θ

Tan (90 – θ) = Cot θ

Cot ( 90 – θ) = Tan θ

Sec (90 – θ) = Csc θ

Csc (90 – θ) = Sec θ

Trigonometric Identities of Supplementary Angles

sin (180°- θ) = sinθ

cos (180°- θ) = -cos θ

cosec (180°- θ) = cosec θ

sec (180°- θ)= -sec θ

tan (180°- θ) = -tan θ

cot (180°- θ) = -cot θ

Sum and Difference of Angles Trigonometric Identities

sin(α+β)=sin(α).cos(β)+cos(α).sin(β)

sin(α–β)=sinα.cosβ–cosα.sinβ

cos(α+β)=cosα.cosβ–sinα.sinβ

cos(α–β)=cosα.cosβ+sinα.sinβ