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Mathematics
Mathematics
Problem
Consider
P
=
arcsin
(
1
3
)
+
arcsin
(
2
2
3
)
P=\arcsin\left(\dfrac{1}{3}\right)+\arcsin\left(\dfrac{2\sqrt{2}}{3}\right)
P
=
arcsin
(
3
1
)
+
arcsin
(
3
2
2
)
. a. (i) Show that
sin
P
=
1
\sin P = 1
sin
P
=
1
. b. (ii) Deduce the exact principal value of
P
P
P
. c. (iii) Hence evaluate
arccos
(
1
2
)
−
P
\arccos\left(\dfrac{1}{\sqrt{2}}\right)-P
arccos
(
2
1
)
−
P
, giving your answer in simplest exact form.
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