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Mathematics
Mathematics
Problem
If
log
x
=
−
1
3
\log x = \frac{-1}{3}
lo
g
x
=
3
−
1
,
log
y
=
2
5
\log y = \frac{2}{5}
lo
g
y
=
5
2
and
P
=
log
(
sin
(
arccos
1
−
x
2
)
)
P = \log (\sin(\arccos \sqrt{1-x^2}))
P
=
lo
g
(
sin
(
arccos
1
−
x
2
))
,
Q
=
log
(
cos
(
arctan
1
−
x
2
y
2
x
y
)
)
Q = \log \left( \cos \left( \arctan \frac{\sqrt{1-x^2 y^2}}{xy} \right) \right)
Q
=
lo
g
(
cos
(
arctan
x
y
1
−
x
2
y
2
)
)
, then a.
P
=
−
1
9
P = \frac{-1}{9}
P
=
9
−
1
b.
P
+
Q
=
−
4
15
P + Q = \frac{-4}{15}
P
+
Q
=
15
−
4
c.
P
−
Q
=
−
2
5
P - Q = \frac{-2}{5}
P
−
Q
=
5
−
2
d.
P
Q
=
−
5
\frac{P}{Q} = -5
Q
P
=
−
5
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