What is a trigonometric identity How and why do we use trigo

What is a trigonometric identity? How and why do we use trigonometric identities in mathematics? How can you verify an identity? Give some examples.

Solution

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables where both sides of the equality are defined
Sometimes it is possible to write some complex trignmetric functions in really simple form fr example instead f writing Sinx/Cosx we can write that as Tanx so as we can see here it is easy to identify Tanx rather than first finding Sinx and then finding Cosx and then divide them to get our answer
Here is an example below:
we need to prove that left side is equal to right side
cot x/csc x=cos x
So let us simplify left side,
(cos x/sin x)/(1/sin x)
applying keep change flip
(cos x/sin x)*sin x
now we can cancel out sin x
so we are left with cos x
which is equal to right side of the equation
hence proved.