Sum & Difference Identities And The Values Chart Worksheet With Answer Key Page 3
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4Sum & Difference Identities and the Values Chart
KEY
Rewrite each expression in terms of only. To do this, apply the sum or difference identities to
each expression, substitute known values from the values chart, and simplify.
Expression
Apply Identity and Substitute
Simplify
e
j
2
2
sin cos
cos sin
cos
sin
Ex: sin
4
4
2
2
4
2
2
2
2
a
f
sin �� cos 30° − cos �� sin 30°
1. sin
30
√ 3
1
sin �� −
cos ��
√ 3
1
2
2
2
2
��
��
cos �� cos
− sin �� sin
e j
2
2
− sin ��
2. cos
0
1
2
a
f
sin 60° cos �� + cos 60° sin ��
3. sin 60
√ 3
1
cos �� +
sin ��
√ 3
1
2
2
2
2
a
f
cos 60° cos �� + sin 60° sin ��
4. cos 60
1
√ 3
cos �� +
sin ��
√ 3
1
2
2
2
2
a
f
sin �� cos 45° − cos �� sin 45°
5. sin
45
√ 2
√ 2
sin �� −
cos ��
√ 2
√ 2
2
2
2
2
��
��
cos �� cos
+ sin �� sin
e j
4
4
√ 2
√ 2
6. cos
cos �� +
sin ��
√ 2
√ 2
4
2
2
2
2
��
��
sin �� cos
− cos �� sin
e
j
6
6
√ 3
1
7. sin
sin �� +
cos ��
√ 3
1
6
2
2
2
2
a
f
sin 45° cos �� + cos 45° sin ��
8. sin 45
√ 2
√ 2
cos �� +
sin ��
√ 2
√ 2
2
2
2
2
a
f
cos 45° cos �� − sin 45° sin ��
9. cos 45
√ 2
√ 2
cos �� −
sin ��
√ 2
√ 2
2
2
2
2
��
��
sin
cos �� − cos
sin ��
e
j
4
4
√ 2
√ 2
10. sin
cos �� −
sin ��
√ 2
√ 2
4
2
2
2
2
a
f
sin 180° cos �� + cos 180° sin ��
11. sin 180
− sin ��
–1
0
��
��
cos �� cos
− sin �� sin
e
j
6
6
√ 3
1
12. cos
cos �� −
sin ��
√ 3
1
6
2
2
2
2
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