find the general solution of the equation cos4x=cos2x
Answers
Answer:
apako para hogs na
Maine muze nahi aatta iisi lea eeyisa likha khuch log to ata to nahi lekin likhate haiisssshbn
Answer:
cos4x=cos2x
cos4x−cos2x=0
we know that cosx−cosy=−2sin
2
x+y
sin
2
x−y
Replacing x with 4x and y with 2x
−2sin(
2
4x+2x
)sin(
2
4x−2x
)=0
−2sin(
2
6x
)sin(
2
2x
)=0
−2sin3xsinx=0
sin3xsinx=
−2
0
sin3xsinx=0
So, either sin3x=0 or sinx=0
We solve sin3x=0 & sinx=0 separately
General solution for sin3x=0
Let sinx=siny ___(1)
sin3x=sin3y ___(2)
Given sin3x=0
From (1) and (2)
sin3y=0
sin3y=sin(0)
3y=0 ___(3)
y=0 ___(4)
General solution for sin3x=sin3y is
3x=nπ±(−1)
n
3y where n∈Z
Putting y=0
3x=nπ±(−1)
n
0
3x=nπ
x=
3
nπ
where n∈Z
General solution for sinx=0
Let sinx=siny
Given sinx=0
From (1) and (2)
siny=0
siny=sin(0)
y=0
General solution for sinx=siny is
x=nπ±(−1)
n
y where n∈Z
putting y=0
x=nπ±(−1)
n
0
x=nπ where n∈Z
Therefore,
General Solution are
For sin3x=0,x=
3
nπ
Or
For sinx=0,x=nπ
Where n∈Z