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Sum and Difference Identities
The Identities
In trigonometry, there are six sum and difference identities. They are useful when the given angle in a trigonometry expression cannot be evaluated. The six sum and difference identities are given as:
1.)
2.)
3.)
4.)
5.)
6.)
Example Problem
Evaluate the following trigonometry expressions by using the sum and difference identities.
1.)
2.)
3.)
Solution:
To evaluate the angle without a calculator we can use
–
.
This means we use the difference identities where a – b = –
. Therefore, a =
and b =
.
1.)
The final answer is or 0.259.
2.)
The final answer is or 0.966.
3.)
The final answer is or 0.268.