Answer:
Consider the given equation.
4sinxsin2xsin4x=sin3x
2(2sin2xsinx)sin4x=sin3x
We know that
2sinAsinB=cos(A−B)−cos(A+B)
Therefore,
2[cos(2x−x)−cos(2x+x)]sin4x=sin3x
2[cosx−cos3x]sin4x=sin3x
2sin4xcosx−2sin4xcos3x=sin3x
We know that
2sinAcosB=sin(A+B)+sin(A−B)
Therefore,
sin(4x+x)+sin(4x−x)−[sin(4x+3x)+sin(4x−3x)]=sin3x
sin(5x)+sin(3x)−[sin(7x)+sin(x)]=sin3x
sin(5x)−sin(7x)=sin(x)
We know that
sinC−sinD=2cos(
2
C+D
)sin(
2
C−D
)
Therefore,
2cos(
2
5x+7x
)sin(
2
5x−7x
)=sinx
2cos(
2
12x
)sin(
2
−2x
)=sinx
2cos(6x)sin(−x)=sinx
−2cos(6x)sin(x)=sinx
cos6x=−
2
1
6x=2nπ±
3
2π
x=
3
nπ
±
9
π
Hence, the value is
3
nπ
±
9
π
.
Answer:
0
Step-by-step explanation:
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Solution:
The numbers are given below as
To figure out the common ratio, we will use the formula below
By substituting the values, we will have
Hence,
The final answer is
The type of sequence is GEOMETRIC
The common ratio is 2/5