Evaluate Sec 15 Cos 15
Answers
Answered by
0
Answer:
hhhhhhhhhhhhhhhhhhiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
Answered by
0
Answer:
Explanation:
This is one of those rare questions that you can evaluate exactly using the sum and différence formulas.
First, though, let's define
sec
θ
. By the reciprocal identities
sec
θ
=
1
cos
θ
sec
15
=
1
cos
15
Now,
15
∘
can be written as
60
∘
−
45
∘
By the sum and différence identity
cos
(
α
−
θ
)
=
cos
α
cos
θ
+
sin
α
sin
θ
We can therefore state the following:
1
cos
15
=
1
cos
(
60
−
45
)
Expanding:
=
1
cos
60
cos
45
+
sin
60
sin
45
=
1
1
2
×
1
√
2
+
√
3
2
×
1
√
2
=
1
(
1
2
√
2
+
√
3
2
√
2
)
=
1
1
+
√
3
2
√
2
=
2
√
2
1
+
√
3
Rationalizing the denominator:
=
2
√
2
1
+
√
3
×
1
−
√
3
1
−
√
3
=
2
√
2
−
2
√
6
−
2
=
2
(
√
2
−
√
6
)
−
2
=
√
6
−
√
2
Therefore,
sec
15
=
√
6
−
√
2
Hopefully this helps!
Similar questions