sec theta -1/sec theta +1 = 1- cos theta/1+ cos theta
Answers
Answer:
±
sin
θ
Explanation:
√
(
1
−
cos
θ
)
(
1
+
cos
θ
)
Recall: (1-costheta)(1+costheta) is an example of the difference of 2 squares. The general form is
(
a
−
b
)
(
a
+
b
)
=
a
2
−
b
2
=
√
1
−
cos
2
θ
Recall:
sin
2
θ
+
cos
2
θ
=
1
so,
1
−
cos
2
θ
=
sin
2
θ
=
√
sin
2
θ
When you are square rooting a number, it can be positive or negative. Why?
Here's an example
2
2
=
4
and
(
−
2
)
2
=
4
If you square a negative or positive number, its result will always be positive unless its a complex number.
=
±
sin
θ
Alan P.
May 20, 2018
Answer:
√
(
1
−
cos
(
θ
)
)
(
1
+
cos
(
θ
)
)
=
|
sin
(
θ
)
|
Explanation:
Based on the Pythagorean Theorem we know (or maybe you just simply remember)
XXX
cos
2
(
θ
)
+
sin
2
(
θ
)
=
1
or
XXX
1
−
cos
2
(
θ
)
=
sin
2
(
θ
)
(
1
−
a
)
(
1
+
a
)
=
1
−
a
2
or, in this case
(
1
−
cos
(
θ
)
)
(
1
+
cos
(
θ
)
)
=
1
−
cos
2
(
θ
)
which we have already noted is the same as
XXXXXXXXXXXXXX
=
sin
2
(
θ
)
So
√
(
1
−
cos
(
θ
)
)
(
1
+
cos
(
θ
)
)
=
√
sin
2
(
θ
)
and since the square root symbol always implies the positive root
XXXXXXXXXXXXXXXXX
=
|
sin
(
θ
)
|Answer:
±
sin
θ
Explanation:
√
(
1
−
cos
θ
)
(
1
+
cos
θ
)
Recall: (1-costheta)(1+costheta) is an example of the difference of 2 squares. The general form is
(
a
−
b
)
(
a
+
b
)
=
a
2
−
b
2
=
√
1
−
cos
2
θ
Recall:
sin
2
θ
+
cos
2
θ
=
1
1
(
θ
)
(
1
−
a
)
(
1
+
a
)
=
1
−
a
2
or, in this case
(
1
−
cos
(
θ
)
)
(
1
+
cos
(
θ
)
)
=
1
−
cos
2
(
θ
)
which we have already noted is the same as
XXXXXXXXXXXXXX
=
sin
2
(
θ
)
So
√
(
1
−
cos
(
θ
)
)
(
1
+
cos
(
θ
)
)
=
√
sin
2
(
θ
)
and since the square root symbol always implies the positive root
XXXXXXXXXXXXXXXXX
=
|
sin
(
θ
)
|
Here is your answer,
