Question

What is trigonometric identity with example?

Answer 1

Define trigonometric identity.

• Trigonometric identities are useful whenever trigonometric functions are used in an expression or equation.
• Any value is valid for identity inequalities present on both sides of an equation.
• These identities are involved in some geometric functions of one or more angles.
• The side length, as well as the angle of a triangle, have several different identities. Only the right-angle triangle is subject to the trigonometric identities.
• The six fundamental trigonometric ratios are sine, cosine, tangent, cosecant, secant, and cotangent.
• The adjacent, opposite, and hypotenuse sides of the right triangle are used to describe all of these trigonometric ratios.

Examples of fundamental trigonometric identities:

1. $\begin{array}{rcl}1.\mathrm{Sin}\mathrm{\theta }& =& \frac{1}{\mathrm{Cosec}\mathrm{\theta }}\\ 2.\cos \mathrm{\theta }& =& \frac{1}{\mathrm{Sec}\mathrm{\theta }}\\ 3.\tan \mathrm{\theta }& =& \frac{1}{\mathrm{Cot}\mathrm{\theta }}\\ 4.\mathrm{Cosec}\mathrm{\theta }& =& \frac{1}{\sin \mathrm{\theta }}\\ 5.\mathrm{Sec}\mathrm{\theta }& =& \frac{1}{\cos \mathrm{\theta }}\\ 6.\mathrm{Cot}\mathrm{\theta }& =& \frac{1}{\tan \mathrm{\theta }}\end{array}$