Proving Angle Addition/Subtraction Formulas
Precalculus · Flashcards
PRECALCULUS · FLASHCARDS
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QUESTION
What is
cos
(
α
+
β
)
\cos(\alpha+\beta)
cos
(
α
+
β
)
if
cos
α
=
4
5
\cos\alpha=\frac{4}{5}
cos
α
=
5
4
,
sin
α
=
3
5
\sin\alpha=\frac{3}{5}
sin
α
=
5
3
,
cos
β
=
12
13
\cos\beta=\frac{12}{13}
cos
β
=
13
12
,
sin
β
=
5
13
\sin\beta=\frac{5}{13}
sin
β
=
13
5
?
QUESTION
Find
tan
(
α
+
β
)
\tan(\alpha+\beta)
tan
(
α
+
β
)
if
tan
α
=
1
2
\tan\alpha=\frac{1}{2}
tan
α
=
2
1
and
tan
β
=
1
3
\tan\beta=\frac{1}{3}
tan
β
=
3
1
.
QUESTION
Find
tan
(
α
−
β
)
\tan(\alpha-\beta)
tan
(
α
−
β
)
if
tan
α
=
2
\tan\alpha=2
tan
α
=
2
and
tan
β
=
1
3
\tan\beta=\frac{1}{3}
tan
β
=
3
1
.
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ANSWER
1
1
1
. Use tangent subtraction:
2
−
1
3
1
+
2
⋅
1
3
=
5
3
5
3
=
1
\frac{2-\frac{1}{3}}{1+2\cdot\frac{1}{3}}=\frac{\frac{5}{3}}{\frac{5}{3}}=1
1
+
2
⋅
3
1
2
−
3
1
=
3
5
3
5
=
1
.
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