The reciprocal relation between any two trigonometric functions is called a reciprocal identity.

Every trigonometric function has a reciprocal relation with another trigonometric function. So, the six trigonometric functions form six reciprocal trigonometric identities in trigonometry and they are used as formulas in mathematics.

Sine has a reciprocal relation with Co-secant function and also Cosecant function also has reciprocal relation with sine function.

$(1)\,\,\,\,\,\,$ $\sin{\theta} = \dfrac{1}{\csc{\theta}}$

$(2)\,\,\,\,\,\,$ $\csc{\theta} = \dfrac{1}{\sin{\theta}}$

Cosine function has a reciprocal relation with Secant function and also Secant function also has reciprocal relation with cosine function.

$(3)\,\,\,\,\,\,$ $\cos{\theta} = \dfrac{1}{\sec{\theta}}$

$(4)\,\,\,\,\,\,$ $\sec{\theta} = \dfrac{1}{\cos{\theta}}$

Similarly, Tangent function has a reciprocal relation with Cotangent function and also Cotangent function also has reciprocal relation with Tangent function.

$(5)\,\,\,\,\,\,$ $\tan{\theta} = \dfrac{1}{\cot{\theta}}$

$(6)\,\,\,\,\,\,$ $\cot{\theta} = \dfrac{1}{\tan{\theta}}$

List of most recently solved mathematics problems.

Jul 04, 2018

Limit (Calculus)

Evaluate $\displaystyle \large \lim_{x \,\to\, \tan^{-1}{3}} \normalsize {\dfrac{\tan^2{x}-2\tan{x}-3}{\tan^2{x}-4\tan{x}+3}}$

Jun 23, 2018

Limit (Calculus)

Evaluate $\displaystyle \large \lim_{x \to 0} \normalsize \dfrac{e^{x^2}-\cos{x}}{x^2}$

Jun 22, 2018

Integral Calculus

Evaluate $\displaystyle \int \dfrac{1+\cos{4x}}{\cot{x}-\tan{x}} dx$

Jun 21, 2018

Limit

Evaluate $\displaystyle \large \lim_{x \to \infty} \normalsize {\sqrt{x^2+x+1}-\sqrt{x^2+1}}$

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.