VERIFYING TRIGONOMETRIC IDENTITIES
Example 1:
Verify the identity
Let's assume that the left side of the identity is the "more complicated" one. Therefore, we will try to
change it to look like the right side.
What could we do to the left side?
1.
2.
3.
4.
5.
Add or subtract trigonometric expressions? NO
Multiply trigonometric expressions? NO
Factor trigonometric expressions? NO
Separate rational trigonometric expressions? NO
Use fundamental identities to rewrite an expression? YES
Let's change cot x to sines and cosines as follows:
and then we multiply
Now what could we do?
1.
2.
3.
4.
5.
Add or subtract trigonometric expressions? YES
Multiply trigonometric expressions? NO
Factor trigonometric expressions? NO
Separate rational trigonometric expressions? NO
Use fundamental identities to rewrite an expression? NO
Let's use the common denominator sin x
What now?
1.
2.
3.
4.
5.
Add or subtract trigonometric expressions? NO
Multiply trigonometric expressions? NO
Factor trigonometric expressions? NO
Separate rational trigonometric expressions? NO
Use fundamental identities to rewrite an expression? YES
Given the Pythagorean Identity
and given the Reciprocal Identity
the right side because
, we can write
, we can show that the left side equals