10.
Express sin
2sinx+3cosx/√13
in simplest form
Answers
Answer:
Step-by-step explanation:
tan
−1
1−sinx
cosx
Calculate cos x & 1-sin x .
As cos2x=cos
2
x−sin
2
x.
cos2(
2
x
)=cos
2
2
x
−sin
2
2
x
cosx=cos
2
2
x
−sin
2
2
x
Similarly sinx=2sin
2
x
cos
2
x
Now
tan
−1
[
1−(2sin
2
x
cos
2
x
)
cos
2
2
x
−sin
2
2
x
]
tan
−1
[
cos
2
2
x
+sin
2
2
x
−2sin
2
x
cos
2
x
cos
2
2
x
−sin
2
2
x
]
tan
−1
[
(cos
2
x
−sin
2
x
)
2
(cos
2
x
+sin
2
x
)(cos
2
x
−sin
2
x
)
]
tan
−1
[
cos
2
x
−sin
2
x
cos
2
x
+sin
2
x
]
tan
−1
[
cos
2
x
−sin
2
x
/cos
2
x
cos
2
x
+sin
2
x
/cos
2
x
]
tan
−1
[
1−tan
2
x
1+tan
2
x
]
tan
−1
(
1−tan
4
π
tan
2
x
tan
4
π
+tan
2
x
)
=tan
−1
[tan(
4
π
+
2
x
)]
=
4
π
+
2
x
.