6.5 Basic Trigonometric Identities. Objective: Develop basic trigonometric identities. Trigonometric Identities. Trigonometric identities are equations that are true for all values of the variable for which the equation is defined. They are most often used to simplify an expression.
Develop basic trigonometric identities.
Be very careful when using Pythagorean identities, the expressions must be squared:
This problem utilizes two identities:
Two identities are also used here:
This problem required first factoring the top and using the identity:
After the substitution, the bottom was factored and the top rearranged. Canceling like terms gives the answer shown.
Here the expression has a GCF factored out first. Then a substitution is made with this identity:
Then the reciprocal identity is used and like terms are canceled. Finally, the reciprocal identity is used again.