How do you solve $Sin (4 theta)= cos(2theta)$ ?

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Answer 1 · 2016-05-02T13:01:49

$theta=(2n+1)pi/4$ or

$theta=npi/2+(-1)^npi/12$

$sin(4theta)=cos(2theta)$

or $2sin(2theta)cos(2theta)-cos(2theta)=0$

or $cos(2theta){2sin(2theta)-1}=0$

i.e. either $cos(2theta)=0$ or $2sin(2theta)-1=0$

If $cos(2theta)=0$ , $2theta=(2n+1)pi/2$ or $theta=(2n+1)pi/4$

and if $2sin(2theta)-1=0$ , we have $sin(2theta)=1/2$

and $2theta=npi+(-1)^npi/6$ or $theta=npi/2+(-1)^npi/12$

How do you solve Sin (4 theta)= cos(2theta)Sin (4 theta)= cos(2theta)?