prove that
(sin x + cos x)^2= 1+sin 2x
Answers
Answered by
1
Step-by-step explanation:
This result follows almost directly from the following:
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
sin
2
(
x
)
+
cos
2
(
x
)
=
1
sin
(
2
x
)
=
2
sin
(
x
)
cos
(
x
)
With these, we have
(
sin
(
x
)
+
cos
(
x
)
)
2
=
sin
2
(
x
)
+
2
sin
(
x
)
cos
(
x
)
+
cos
2
(
x
)
=
(
sin
2
(
x
)
+
cos
2
(
x
)
)
+
2
sin
(
x
)
cos
(
x
)
=
1
+
sin
(
2
x
)
Answered by
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