We'll re-write the condition, multiplying both sides by
the least common denominator, that is the product of denominators of the terms from the
left side: cos2pi*sin 2pi.
But cos 2pi = 1 and sin 2pi = 0
=> cos2pi*sin 2pi = 1*0 = 0
cos 4theta/cos2pi+ sin 4
theta/sin2pi=1
(cos2pi*sin 2pi*cos 4theta)/(cos2pi)+
(cos2pi*sin 2pi*sin 4 theta)/(sin2pi)=1*cos2pi*sin
2pi
We'll reduce like
terms:
sin 2pi*cos 4theta+ cos2pi*sin 4 theta
=1*0
sin (2pi + 4theta) =
0
2pi + 4theta = arcsin 0
2pi
+ 4theta = 0
4theta =
-2pi
theta = -2pi/4
theta =
-pi/2
Under this conditions, we'll calculate the
expression, having theta= -pi/2.
cos4pi/cos2*(-pi/2)+ sin 4
pi/sin2*(-pi/2)
cos -pi = cos pi =
-1
sin -pi = -sin pi = 0
-1/-1
+ 0/0
Since the second fraction is
meaningless (we cannot divide by 0), the expression cannot be computed under this
conditions.
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