If $2 \cos ^{2} heta+3 \cos heta=2$, then permissible value of $\cos heta$ is

Question

If $2 \cos ^{2} 	heta+3 \cos 	heta=2$, then permissible value of $\cos 	heta$ is

Aicharya · Accepted Answer

We have $2 \cos ^{2} 	heta+3 \cos 	heta=2$ $2 \cos ^{2} 	heta+4 \cos 	heta-\cos 	heta-2=0 \Rightarrow 2 \cos 	heta(\cos 	heta+2)-1(\cos 	heta+2)=0$ $(2 \cos 	heta-1)(\cos 	heta+2)=0$ $	herefore \cos 	heta=\frac{1}{2},-2($ Impossible $) \Rightarrow \cos 	heta=\frac{1}{2}$

If $2 \cos ^{2} \theta+3 \cos \theta=2$, then permissible value of $\cos \theta$ is

Solution