# Trigonometric Identities

If we have an equation which contains one or more variables and it is valid for replacement of the values in which both sides of equation is defined then the equation is said to be an identity. The equalities that include the Trigonometric Functions are known as trigonometric identities. Some Functions and angles are also included in trigonometric function. These identities are not similar to the triangle identities.
Now we will talk about the list of trigonometric identities.
The list of trigonometric identity is given below:
First we see even – odd identities of trigonometric function:
Sin (-r) = - sin r;
Cos (-r) = cos r;
Tan (-r) = - tan r;
Cosec (-r) = - cosec r;
Sec (-r) = sec r;
Cot (-r) = - cot r;
These are even – odd identities,
Now we will discuss sum – difference formula:
Sin (r + s) = sin r cos s + cos r sin s;
Cos (r + s) = cos r cos s + sin r sin s;
Tan (r + s) =
These are the sum – difference formulas.
Now we will talk about the fundamental trigonometric identities.
First we will see the Reciprocal Identities of the trigonometric functions:
Sin r =
Cos r =
Tan r =
Cosec r =
Sec r =
Cot r =
These are reciprocal identities.
We will now talk about Pythagorean Identities:
Sin2 r + Cos2 r = 1;
1 + tan2 r = sec2 r;
1 + cot2 r = cosec2 r;
These are Pythagorean identities;
The co – function identities for the fundamental trigonometric function are:
Sin (⊼ / 2 – r) = Cos r;
Cos (⊼ / 2 – r) = Sin r;
Tan (⊼ / 2 – r) = Cot r;
Cosec (⊼ / 2 – r) = Sec r;
Sec (⊼ / 2 – r) = Cosec r;
Cot (⊼ / 2 – r) = Tan r;
These are the co – function identities,
This is all about trigonometric identities.

## Sums as Products

Digital electronics deals with different digital circuits. The digital circuits include various logic gates. Logic gates are defined as the gates used for the implementation of digital circuits. These works on Boolean values that are 0 and 1. There are six logic gates that are AND, OR, NOT, NOR, NAND, XOR and XNOR.
AND gate is defined as the product of various inputs, ...Read More

## Pythagorean Identities

A right angled triangle is a triangle which has Right Angle (900) as one of its angle. The side opposite to right angle is called hypotenuse and is  longest side of the triangle. Side with an angle of 900 is called known as perpendicular and other side is termed as base. Pythagorean Theorem, states that Square of the hypotenuse is equal to sum of squares of the ba...Read More

## Sum and difference formulas

Trigonometry is defined as a stream of mathematics that deals with relationship between the angles and sides of a triangle. This stream is applied over Right Angle triangle, which consist three sides particularly defined as perpendicular, base and hypotenuse. Accordingly, they are categorized into six Functions known as sine function, Cosine function, tangent...Read More

## Double Angle Formulas

In mathematics, trigonometry shows the relationship between the angle and sides of a triangle. Here, we will see the double angle formulas. The double angle formula is given by:
⇒sin α/ 2 = 2 sin α cos α
⇒cos 2 α = cos2 α – sin2α;
Cos 2 α have three formulas which are as follows:
⇒cos 2 α = cos2 α – sin2α;
⇒cos 2 α = 2 cos2 α – 1; and
⇒cos α = 1 – 2 sin2 α;

## Half Angle Formulas

In mathematics, trigonometry is used to show the relationship between the angle and sides of a triangle. Here we will see the half angle formula. The half angle formula is given by:
⇒cos ⊖/ 2 = + √ ½ (1 + cos ⊖), and
⇒sin ⊖/ 2 = + √ ½ (1 - cos ⊖),
Now we will see prove of half angle formulas.
We know that, α is half of 2α, if we put the value 2α in place ...Read More

## Tangent and Cotangent identities

Trigonometry defines various techniques to solve sides and angles problems of a Right Angle triangle. It provides relationship between angles and sides of triangle. It gives various Basic Formulas for finding different angles and sides. It consists of various trigonometric Functions, they are: sine, Cosine, Sec, Cosec, tan and cot. Various identities are...Read More

## Product as Sums

Product of sums is defined as the multiplication of different sum entities. Product is term defined for multiplication and sum is term defined for addition. Combination of both these terms is defined as product of sums. In mathematics, product of sums can be explained by using the identities, like a2-b2 is represented as (a+b) (a-b). This term is written in the form of p...Read More

## Reciprocal Identities

Reciprocal identities are those identities whose inverse are equal to the real Functions. If we talk about, Trig Reciprocal Identities, then this means Trigonometry identities whose reciprocal is equal to real functions. In trigonometry there are mainly six function, sinΘ, cosΘ, tanΘ, cosecΘ, secΘ, and tanΘ. If we see all these then all the function have reciprocal...Read More

## Trigonometric Identities Table

Trigonometry Identities are generally used to measure angles of any triangle whether a right angled triangle, a Equilateral Triangle etc, we have fix basic Trigonometric Functions which are known as Trigonometry identities, they are sine , cosine, tangent, cotangent, secant and cosecant. All these are very important to find angles of triangle or any other ...Read More

## Verify Trigonometric Identities

Trigonometric Identities are formulae that are formed using six trigonometric Functions: sine, cosine, tangent, cotangent, secant and cosecant. Verify Trigonometric Identities, means validating proofs of trigonometric formulas. So, Trigonometric Identities proof for various identities can be given as follows:
1.      cos A * tan A = sin A,