what is sinX + cosX answer only one user
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Answer:
Suppose that
sin
x
+
cos
x
=
R
sin
(
x
+
α
)
Then
sin
x
+
cos
x
=
R
sin
x
cos
α
+
R
cos
x
sin
α
=
(
R
cos
α
)
sin
x
+
(
R
sin
α
)
cos
x
The coefficients of
sin
x
and of
cos
x
must be equal so
R
cos
α
=
1
R
sin
α
=
1
Squaring and adding, we get
R
2
cos
2
α
+
R
2
sin
2
α
=
2
so
R
2
(
cos
2
α
+
sin
2
α
)
=
2
R
=
√
2
And now
cos
α
=
1
√
2
sin
α
=
1
√
2
so
α
=
cos
−
1
(
1
√
2
)
=
π
4
sin
x
+
cos
x
=
√
2
sin
(
x
+
π
4
)
Explanation:
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