The reciprocal relation of a trigonometric function with another trigonometric function is called reciprocal identity.
Every trigonometric function has a reciprocal relation with another trigonometric function. So, the six trigonometric ratios form six reciprocal trigonometric identities and they are used as formulas in trigonometric mathematics.
Sin function is a reciprocal function of cosecant and cosecant function is also a reciprocal of sine function.
$(1)\,\,\,\,\,\,$ $\sin{\theta} = \dfrac{1}{\csc{\theta}}$
$(2)\,\,\,\,\,\,$ $\csc{\theta} = \dfrac{1}{\sin{\theta}}$
Cos function is a reciprocal function of secant and secant function is also a reciprocal of cosine function.
$(3)\,\,\,\,\,\,$ $\cos{\theta} = \dfrac{1}{\sec{\theta}}$
$(4)\,\,\,\,\,\,$ $\sec{\theta} = \dfrac{1}{\cos{\theta}}$
Tan function is a reciprocal function of cotangent and cot function is also a reciprocal of tangent function.
$(5)\,\,\,\,\,\,$ $\tan{\theta} = \dfrac{1}{\cot{\theta}}$
$(6)\,\,\,\,\,\,$ $\cot{\theta} = \dfrac{1}{\tan{\theta}}$
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