Reciprocal Identities of Trigonometry
The simplest and most basic trigonometric identities are those involving the reciprocals of the trigonometry
functions. For simplicty a reciprocal of a number is equals 1 divided by that
number — for example, the reciprocal of 4 is 1/4. Another way to describe
reciprocals is to point out that the product of a number and its reciprocal is always
equals to 1.
When we multiply the reciprocals together, we get
1:
SinӨ x CosecӨ = 1
CosӨ x SecӨ =
1
Tan Ө x CotӨ = 1
There is an exception, that the function
can’t be equal to 0; as the number 0 doesn’t have a reciprocal as it will become
Infinity.
The reciprocal identity is a very useful one
when we are solving trigonometric equations. If we find a way to multiply each
side of an equation by a function’s reciprocal, we may be able to reduce some
part of the equation to 1 — and simplifying is always a good thing in Mathematics.