Question

Write the trigonometric identities. ​

Answer 1

Answer:

Reciprocal Identities

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 Identities

sin2 a + cos2 a = 1

1+tan2 a  = sec2 a

cosec2 a = 1 + cot2 a

Ratio Identities

Tan θ = Sin θ/Cos θ

Cot θ = Cos θ/Sin θ

Opposite Angle Identities

Sin (-θ) = – Sin θ

Cos (-θ) = Cos θ

Tan (-θ) = – Tan θ

Cot (-θ) = – Cot θ

Sec (-θ) = Sec θ

Csc (-θ) = -Csc θ

θ

Complementary Angles Identities

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

Angle Sum and Difference Identities

Consider two angles , α and β, the trigonometric sum and difference identities are as follows:

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

tan(α+β)=tanα+tanβ1–tanα.tanβ

tan(α–β)=tanα–tanβ1+tanα.tanβ

Answer 2

Reciprocal Identities
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 Identities
sin2 a + cos2 a = 1
1+tan2 a = sec2 a
cosec2 a = 1 + cot2 a
Ratio Identities
Tan θ = Sin θ/Cos θ
Cot θ = Cos θ/Sin θ
Opposite Angle Identities
Sin (-θ) = – Sin θ
Cos (-θ) = Cos θ
Tan (-θ) = – Tan θ
Cot (-θ) = – Cot θ
Sec (-θ) = Sec θ
Csc (-θ) = -Csc θ
Complementary Angles Identities
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
Angle Sum and Difference Identities
Consider two angles , α and β, the trigonometric sum and difference identities are as follows:

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
tan(α+β)=tanα+tanβ1–tanα.tanβ
tan(α–β)=tanα–tanβ1+tanα.tanβ