# Trigonometric identities

Trigonometric identities are mathematical equations involving trigonometric functions (such as sine, cosine, tangent, cotangent, secant, and cosecant) that hold true for all values of the variables within their respective domains. Trigonometric identities are widely used in mathematics, physics, and engineering to simplify and manipulate trigonometric expressions and solve trigonometric equations.

Here are some common trigonometric identities:

### Pythagorean Identities

$sin^2(x) + cos^2(x) = 1$ $tan^2(x) + 1 = sec^2(x)$ $cot^2(x) + 1 = csc^2(x)$### Reciprocal Identities

$csc(x) = 1/sin(x)$ $sec(x) = 1/cos(x)$ $cot(x) = 1/tan(x)$### Quotient Identities

$tan(x) = sin(x)/cos(x)$ $cot(x) = cos(x)/sin(x)$Co-function Identities:

$sin(pi/2 - x) = cos(x)$ $cos(pi/2 - x) = sin(x)$ $tan(pi/2 - x) = cot(x)$ $csc(pi/2 - x) = sec(x)$ $sec(pi/2 - x) = csc(x)$ $cot(pi/2 - x) = tan(x)$### Double Angle Identities

$$$$ $sin(2x) = 2sin(x)cos(x)$ $cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1 = 1 - 2sin^2(x)$ $tan(2x) = (2tan(x))/(1 - tan^2(x))$### Sum and Difference Identities

$sin(x + y) = sin(x)cos(y) + cos(x)sin(y)$ $cos(x + y) = cos(x)cos(y) - sin(x)sin(y)$ $tan(x + y) = (tan(x) + tan(y))/(1 - tan(x)tan(y))$ $sin(x - y) = sin(x)cos(y) - cos(x)sin(y)$ $cos(x - y) = cos(x)cos(y) + sin(x)sin(y)$ $tan(x - y) = (tan(x) - tan(y))/(1 + tan(x)tan(y))$These are just some of the many trigonometric identities that are used in mathematics. Familiarizing yourself with these identities and understanding how to apply them can be helpful in solving trigonometric equations, simplifying trigonometric expressions, and analyzing trigonometric functions.