prove that cos^2 A + tan^2 A = 1
Answers
Answered by
15
Answer:
The answer2 are:
x
=
k
π
and
π
4
+
k
π
.
The equation can be written:
cos
2
x
+
cos
2
x
tan
2
x
=
1
⇒
cos
2
x
+
cos
2
x
sin
2
x
cos
2
x
=
1
⇒
cos
2
x
+
sin
2
x
=
1
⇒
sin
2
x
+
cos
2
x
=
1
.
Now it is possible multiply both members for
√
2
2
:
√
2
2
sin
2
x
+
√
2
2
cos
2
x
=
√
2
2
⇒
sin
2
x
cos
(
π
4
)
+
cos
2
x
sin
(
π
4
)
=
√
2
2
.
Using the addition formula:
sin
(
2
x
+
π
4
)
=
√
2
2
.
The sinus is
√
2
2
if its argument is
π
4
+
2
k
π
or
3
4
π
+
2
k
π
.
So:
2
x
+
π
4
=
π
4
+
2
k
π
⇒
2
x
=
2
k
π
⇒
x
=
k
π
,
and
2
x
+
π
4
=
3
4
π
+
2
k
π
⇒
2
x
=
π
2
+
2
k
π
⇒
x
=
π
4
+
k
π
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