Question

what is the value of cos 15

Answer 1

cos
15
˚
can be written as
cos
(
60
˚
−
45
˚
)
. We use the difference formula for cosine that states
cos
(
A
−
B
)
=
cos
A
cos
B
+
sin
A
sin
B
to expand.
cos
15
˚
=
cos
60
˚
cos
45
˚
+
sin
60
˚
sin
45
˚
We know, by the special triangles, that
cos
60
˚
=
1
2
,
cos
45
˚
=
sin
45
˚
=
1
√
2
and
sin
60
˚
=
√
3
2
.
cos
15
˚
=
(
1
2
)
(
1
√
2
)
+
√
3
2
(
1
√
2
)
cos
15
˚
=
1
2
√
2
+
√
3
2
√
2
cos
15
˚
=
1
+
√
3
2
√
2
Hopefully this helps!