A trigonometric fuction is by definition an equation that involves at least one trigonometric function of a variable. Such an equation is called a trigonometric identity if it is true for all values of the variable for which both sides of the equation are defined.
Verifying an identity, or proving that a given equation is an identity, is to show that the left hand side (LHS) of the equation is identical to the right hand side (RHS).
There are 8 Basic Identities:
cscθ=1/sinθ secθ=1/cosθ cotθ=cosθ/sinθ
Pythagorean Identities:
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Verifying Identities means to prove that LHS=RHS
Method One - use the fundamental identities to change each side (split by a vertical line) of the equation until the same form is obtained on each side. Once sides are equal, state that LHS=RHS.
Example 1: Use the fundamental identities to express each in terms of cosθ
Example 2: Without using a calculator, find the value of... 3cos²4π/7sec²4π/7
Example 3: Verify using method one.
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