Unit 3 - Objective 5 - Fundamental Trigonometric Identities
Quick Review

An identity is an equation that is true for all values of the variable. Some basic identities are:



To prove that an identity is true: change either side, or both sides, until the sides are the same.


Example 1

csc theta =

I would work with the right side. Try to get it to look like the left side. Change cot theta to sin theta and cosine s.



You have now proved the identity!


Example 2

sec theta - sec theta sin2 theta = cos theta

I would work with the left side. Factor out a sec theta.

sec theta (1 - sin2 theta) = cos theta

Since sin2 theta + cos2 theta = 1,
cos2 theta = 1 - sin2 theta

So, sec theta (cos2 theta) = cos theta




Example 3




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