If( costheta+iotasintheta)(cos2theta+ iotasin2theta)so on ( cosntheta+iotasinntheta)=1,then the value of theta is
Answer (1)
30th Nov, 2019
(cosx+isinx)*(cos2x+isin2x)**(cosnx+isinnx)=1
The above is our given equation.
Now we have to find the value of x from that.
Now we know the theorem
(cosx1+isinx1)*(cosx2+isinx2)**(cosxn+isinxn)
=cos(x1+X2++xn)+isin(x1+X2++xn)
Hence
(cosx+isinx)*(cos2x+isin2x)**(cosnx+isinnx)=1
cos(xn(n+1)/2)+isin(xn(n+1)/2)=1
hence cos(xn(n+1)/2)=1
hence xn(n+1)/2=2m*pi m is an integer
Sin(xn(n+1)/2)=0
xn(n+1)/2=l*pi l is an integer
Hence x=4m*pi/n(n+1) m is an integer
The above is our given equation.
Now we have to find the value of x from that.
Now we know the theorem
(cosx1+isinx1)*(cosx2+isinx2)**(cosxn+isinxn)
=cos(x1+X2++xn)+isin(x1+X2++xn)
Hence
(cosx+isinx)*(cos2x+isin2x)**(cosnx+isinnx)=1
cos(xn(n+1)/2)+isin(xn(n+1)/2)=1
hence cos(xn(n+1)/2)=1
hence xn(n+1)/2=2m*pi m is an integer
Sin(xn(n+1)/2)=0
xn(n+1)/2=l*pi l is an integer
Hence x=4m*pi/n(n+1) m is an integer
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