How do you use the fundamental trigonometric identities to determine the simplified form of the expression?
"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:
Apply the quotient identity
Reapplying the quotient identity, in reverse form:
Apply the reciprocal identity
Put the denominator on a common denominator:
Rearrange the pythagorean identity
Once again, put on a common denominator:
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.
Simplify the following expressions:
Hopefully this helps, and good luck!