# How do you use the fundamental trigonometric identities to determine the simplified form of the expression?

##### 1 Answer

"The fundamental trigonometric identities" are the basic identities:

•The reciprocal identities

•The pythagorean identities

•The quotient identities

They are all shown in the following image:

When it comes down to simplifying with these identities, we must use combinations of these identities to reduce a much more complex expression to its simplest form.

Here are a few examples I have prepared:

a) Simplify:

Apply the quotient identity

Reapplying the quotient identity, in reverse form:

b) Simplify:

Apply the reciprocal identity

Put the denominator on a common denominator:

Rearrange the pythagorean identity

c) Simplify:

Once again, put on a common denominator:

Multiply out:

Applying the pythagorean identity

Cancelling out the

Applying the reciprocal identity

Finally, on a last note, I know that here in Canada, British Columbia more specifically, these identities are given on a formula sheet, but I don't know what it's like elsewhere. In any event, many students, me included, memorize these identities because they're that important to mathematics. I would highly recommend memorization.

**Practice exercises:**

Simplify the following expressions:

a)

b)

c)

d)

Hopefully this helps, and good luck!