Similar Triangles, Right Triangles, And The Definition Of The Sine, Cosine And Tangent Functions Of Angles Of A Right Triangle Worksheets With Answer Key Page 42

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θ
π
θ
π
θ
π
θ
θ
154. 1
155. cos (
+
) = cos
cos
- sin
sin
= -cos
- 0 = -cos
θ
φ
θ
φ
θ
φ
θ
φ
θ
φ
θ
φ
θ
φ
156. cos (
+
) + cos (
-
) = cos
cos
- sin
sin
+ cos
cos
+ sin
sin
= 2cos
cos
θ
θ
θ
θ
θ
θ
θ
θ
2
2
2
2
2
2
2
2
157. tan
(-
) - sec
= (tan (-
))
- sec
= (-tan
)
- sec
= tan
- sec
= -1
(
)
(
)
(
) (
)
θ
φ
θ
φ
θ
φ
θ
φ
θ
φ
θ
φ
−
−
+
+
−
−
cos
cos
cos
cos
sin
sin
cos
cos
sin
sin
=
158.
(
)
(
)
(
) (
)
θ
φ
θ
φ
θ
φ
θ
φ
θ
φ
θ
φ
−
+
+
+
+
−
cos
cos
cos
cos
sin
sin
cos
cos
sin
sin
θ
φ
2
sin
sin
θ
φ
=
=
tan
tan
θ
φ
2
cos
cos
DOUBLE-ANGLE AND HALF-ANGLE IDENTITIES
θ
φ
+
θ
tan
tan
θ
θ
θ
φ
θ
162.
163.
cos
159. 2sin
cos
160. sin (
-
)
161. cos 2
θ
φ
−
1
tan
tan
2
θ
φ
θ
φ
θ
θ
θ
θ
2
2
2
2
164. sin
cos
+ cos
sin
165. cos
- sin
= 2cos
- 1 = 1 - 2 sin
θ
θ
−
1
cos
θ
θ
φ
±
166.
tan
167. cos 2
168.
169. tan (
-
)
2
2
θ
2
tan
θ
φ
θ
φ
θ
θ
171.
170. sin
cos
- cos
sin
172. cos 2
173. sin 2
θ
−
2
1
tan
6 −
1
2
3
θ
φ
θ
178.
174. sin (
+
)
175. tan 2
176.
177.
2
4
2
1
63
9
2
180.
181.
182.
179.
8
65
7
4
θ
φ
θ
φ
θ
φ
θ
φ
−
−
−
(
)
1
1
tan
tan
1
tan
tan
cot
cot
cot
cot
1
θ
φ
+
=
=
=
⋅
=
183.
cot
(
)
θ
φ
θ
φ
θ
φ
θ
φ
θ
φ
+
+
+
+
tan
tan
tan
tan
tan
cot
cot
cot
cot
θ
θ
θ
θ
−
−
−
2
2
2
2
1
1
tan
1
tan
cot
cot
1
θ
=
=
=
⋅
=
184.
cot
2
θ
θ
θ
θ
θ
2
tan
2
2
tan
2
tan
2
cot
cot
(
)
θ
θ
θ
θ
θ
θ
θ
θ
+
−
+
+
−
2
2
2
sin
cos
1
sin
2
sin
cos
cos
1
2
sin
cos
=
=
=
185.
1
θ
θ
θ
θ
θ
sin
2
2
sin
cos
2
sin
cos
θ
θ
θ
θ
θ
θ
sin
2
2
sin
cos
=
=
=
−
2
2
186.
cos
2
cos
sin
θ
θ
2
sin
2
sin
2
2
2
(
)
θ
θ
θ
θ
θ
θ
θ
θ
θ
θ
θ
θ
=
+
=
+
=
−
+
2
187.
sin
3
sin
2
sin
cos
2
cos
sin
2
sin
1 (
2
sin
)
cos
2 (
sin
cos
)
(
)
θ
θ
θ
θ
θ
θ
θ
θ
=
−
+
=
−
+
−
3
2
3
2
sin
2
sin
2
sin
cos
sin
2
sin
2
sin
1
sin
θ
θ
=
−
3
3
sin
4
sin
- 42 -

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