6. What is the value of 5arccos^-1(1/2) + 7arcsin^-1(- 1/2) ?
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Answer:
4
+
3
√
3
10
.
Explanation:
Let
a
=
a
r
c
sin
(
3
5
)
∈
Q
1
and
b
=
a
r
c
cos
(
1
2
)
∈
Q
1
.
Then,
sin
a
=
3
5
and
cos
a
=
√
1
−
sin
2
a
=
√
1
−
9
25
=
4
5
.
Likewise,
cos
b
=
1
2
and
sin
b
=
√
1
−
cos
2
b
=
√
1
−
1
4
=
√
3
2
.
Now, the given expression is
cos( a - b ) = cos a cos b + sin a sin b
=
(
4
5
)
(
1
2
)
+
(
3
5
)
(
√
3
2
)
=
4
+
3
√
3
10
.
Answer
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