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Byju's Answer
Standard XI
Mathematics
Trigonometric Ratios of Multiples of an Angle
Prove the fol...
Question
Prove the following:
c
o
s
4
x
+
c
o
s
3
x
+
c
o
s
2
x
s
i
n
4
x
+
s
i
n
3
x
+
s
i
n
2
x
=
c
o
t
3
x
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Solution
L
H
S
=
c
o
s
4
x
+
c
o
s
3
x
+
c
o
s
2
x
s
i
n
4
x
+
s
i
n
3
x
+
s
i
n
2
x
=
c
o
s
4
x
+
c
o
s
2
x
+
c
o
s
3
x
s
i
n
4
x
+
s
i
n
2
x
+
s
i
n
3
x
=
2
cos
(
4
x
+
2
x
2
)
cos
(
4
x
−
2
x
2
)
+
c
o
s
3
x
2
sin
(
4
x
+
2
x
2
)
cos
(
4
x
−
2
x
2
)
+
s
i
n
3
x
=
c
o
t
3
x
=
R
H
S
Hence proved
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Similar questions
Q.
cos
4
x
+
cos
3
x
+
cos
2
x
sin
4
x
+
sin
3
x
+
sin
2
x
is equal to -
Q.
Identity transformations of Trigonometric Expressions.
prove the following identities.
s
i
n
2
x
−
s
i
n
3
x
−
s
i
n
4
x
c
o
s
2
x
−
c
o
s
3
x
+
c
o
s
4
x
=
t
a
n
3
x
.
Q.
Let
y
=
cos
x
+
cos
2
x
+
cos
3
x
+
cos
4
x
+
cos
5
x
+
cos
6
x
+
cos
7
x
sin
x
+
sin
2
x
+
sin
3
x
+
sin
4
x
+
sin
5
x
+
sin
6
x
+
sin
7
x
,
then which of the following hold good?
Q.
Solve the following equations:
(i)
cos
x
+
cos
2
x
+
cos
3
x
=
0
(ii)
cos
x
+
cos
3
x
-
cos
2
x
=
0
(iii)
sin
x
+
sin
5
x
=
sin
3
x
(iv)
cos
x
cos
2
x
cos
3
x
=
1
4
(v)
cos
x
+
sin
x
=
cos
2
x
+
sin
2
x
(vi)
sin
x
+
sin
2
x
+
sin
3
=
0
(vii)
sin
x
+
sin
2
x
+
sin
3
x
+
sin
4
x
=
0
(viii)
sin
3
x
-
sin
x
=
4
cos
2
x
-
2
(ix)
sin
2
x
-
sin
4
x
+
sin
6
x
=
0
Q.
Solve:
∫
sin
4
x
+
cos
4
x
sin
3
x
+
cos
3
x
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Trigonometric Ratios of Multiples of an Angle
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