Relationship of Reciprocal Identities

As we know that the product of a number and its reciprocal is always equal to one, we have established similar relationships between the reciprocal identities. The product of a trigonometric function and its reciprocal is equal to 1. Hence, we have

• sin θ × cosec θ = 1
• cos θ × sec θ = 1
• tan θ × cot θ = 1

The above equations establish a relationship between the reciprocal identities of trigonometry for any angle θ and show that the product of a trigonometric function and its reciprocal is equal to 1.

Important Notes on Reciprocal Identities

• sin θ is the reciprocal of cosec θ
• cosec θ is the reciprocal of sin θ
• cos θ is the reciprocal of sec θ
• sec θ is the reciprocal of cos θ
• tan θ is the reciprocal of cot θ
• cot θ is the reciprocal of tan θ