Category: 2. Reciprocal & Co-Functions

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 =…

Now, that we know the reciprocal identities of trigonometry, let us now prove each one of them using the definition of the basic trigonometric functions. First, we will derive the reciprocal identity of the sine function. Consider a right-angled triangle ABC with a right angle at C. We know that sin θ = Perpendicular/Hypotenuse = c/a and cosec…

Reciprocal identities are applied in various trigonometry problems to simplify the calculations. The formulas of the six main reciprocal identities are: sin x = 1/cosec x cos x = 1/sec x tan x = 1/cot x cot x = 1/tan x sec x = 1/cos x cosec x = 1/sin x

The reciprocals of the six fundamental trigonometric functions (sine, cosine, tangent, secant, cosecant, cotangent) are called reciprocal identities. The reciprocal identities are important trigonometric identities that are used to solve various problems in trigonometry. Each trigonometric function is a reciprocal of another trigonometric function. The sine function is the reciprocal of the cosecant function and vice-versa; the cosine function is the reciprocal…

Reciprocal Identities are the reciprocals of the six main trigonometric functions, namely sine, cosine, tangent, cotangent, secant, cosecant. The important thing to note is that reciprocal identities are not the same as the inverse trigonometric functions. Every fundamental trigonometric function is a reciprocal of another trigonometric function. For example, cosecant is the reciprocal identity of the…