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7
Trig Manipulation
Trig Manipulation
Source:
December 22, 2005
trigonometry
quadratics
number theory
relatively prime
algebra
quadratic formula
Problem Statement
Given that
(
1
+
sin
t
)
(
1
+
cos
t
)
=
5
/
4
(1+\sin t)(1+\cos t)=5/4
(
1
+
sin
t
)
(
1
+
cos
t
)
=
5/4
and
(
1
−
sin
t
)
(
1
−
cos
t
)
=
m
n
−
k
,
(1-\sin t)(1-\cos t)=\frac mn-\sqrt{k},
(
1
−
sin
t
)
(
1
−
cos
t
)
=
n
m
−
k
,
where
k
,
m
,
k, m,
k
,
m
,
and
n
n
n
are positive integers with
m
m
m
and
n
n
n
relatively prime, find
k
+
m
+
n
.
k+m+n.
k
+
m
+
n
.
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