Question

what do you mean by trigonometric identities ?

Answer 1

In mathematics, trigonometric identities are equalities that involvetrigonometric functions and are true for every value of the occurring variables where both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.

Answer 2

The Trigonometric Identities are equations that are true for Right Angled Triangles. (If it is not a Right Angled Triangle go to the Triangle Identities page.)

Each side of a right triangle has a name

Adjacent is always next to the angle

And Opposite is opposite the angle

We are soon going to be playing with all sorts of functions, but remember it all comes back to that simple triangle with:

Angle θ

Hypotenuse

Adjacent

Opposite

Sine, Cosine and Tangent

The three main functions in trigonometry are Sine, Cosine and Tangent.

They are just the length of one side divided by another

For a right triangle with an angle θ 

Sine Function:

sin(θ) = Opposite / Hypotenuse

Cosine Function:

cos(θ) = Adjacent / Hypotenuse

Tangent Function:

tan(θ) = Opposite / Adjacent

For a given angle θ each ratio stays the same 
no matter how big or small the triangle is

When we divide Sine by Cosine we get:

sin(θ)cos(θ) = Opposite/HypotenuseAdjacent/Hypotenuse = OppositeAdjacent = tan(θ)

So we can say:

tan(θ) = sin(θ)cos(θ)

That is our first Trigonometric Identity.

Cosecant, Secant and Cotangent

We can also divide "the other way around" (such as Adjacent/Opposite instead of Opposite/Adjacent):

Cosecant Function:

coc(θ) = Hypotenuse / Opposite

Secant Function:

sec(θ) = Hypotenuse / Adjacent

Cotangent Function:

cot(θ) = Adjacent / Opposite

Hope this helps :)