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Problem
Problem
Statement I
If
2
sin
2
x
−
cos
2
x
=
1
2 \sin 2x - \cos 2x = 1
2
sin
2
x
−
cos
2
x
=
1
,
x
≠
(
2
n
+
1
)
π
/
2
x \neq (2n+1)\pi/2
x
=
(
2
n
+
1
)
π
/2
,
n
n
n
is the integer, then
sin
2
x
+
cos
2
x
\sin 2x + \cos 2x
sin
2
x
+
cos
2
x
is equal to
1
/
5
1/5
1/5
.
Statement II
sin
2
x
+
cos
2
x
=
1
+
2
tan
x
−
tan
2
x
1
+
tan
2
x
\sin 2x + \cos 2x = \frac{1 + 2 \tan x - \tan^2 x}{1 + \tan^2 x}
sin
2
x
+
cos
2
x
=
1
+
t
a
n
2
x
1
+
2
t
a
n
x
−
t
a
n
2
x
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