5{ tab2x -cox2x}= 2cos 2x +9 then the value of cos 4x is ..
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Step-by-step explanation:
sec
2
2x=1−tan2x
1+tan
2
2x=1−tan2x
tan
2
2x+tan2x=0
tan2x(tan2x+1)=0
tan2x=0 or tan2x+1=0
Now, tan2x=0
tan2x=tan0
2x=nπ+0,n∈Z
x=
2
nπ
,n∈Z
tan2x+1=0
tan2x=−1=−tan
4
π
=tan(π−
4
π
)=tan
4
3π
2x=nπ+
4
3π
,n∈Z
x=
2
nπ
+
8
3π
,n∈Z
Therefore, the general solution is
2
nπ
or
2
nπ
+
8
3π
,n∈Z
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