How do you solve $sin 2 theta = cos theta$ ?

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Answer 1 · 2018-04-09T08:51:57

$theta=(2n+1)pi/2$ or $theta=npi+-(-1)^npi/6$ , where $n$ is an integer

As $sin2theta=2sinthetacostheta$ , we can write $sin2theta=costheta$ as

$2sinthetacostheta=costheta$

or $2sinthetacostheta-costheta=0$

or $costheta(2sintheta-1)=0$

Hence either $costheta=0$ i.e. $theta=(2n+1)pi/2$ , where $n$ is an integer

or $2sintheta-1=0$ i.e. $sintheta=1/2=sin(pi/6)$

i.e. $theta=npi+-(-1)^npi/6$ , where $n$ is an integer

How do you solve sin 2 theta = cos thetasin 2 theta = cos theta?