Question

solve the quadratic 2cos^2θ - cosθ =1

Answer 1

you can simply:

\[2\cos^2\theta-\cos \theta-1=0\]
Now treat this as a quadratic, simply let cos theta be represented by "a":

\[2a^2-a-1=0\]

Then factor:

\[(2a+1)(a-1)=0\]

Next set each factor to zero:

\[2a+1=0\]
and

\[a-1=0\]

Which means that :

\[a=-1/2\]

and

a=1

Now simply replace "a" with cos:

cos(theta)=-1/2

and

cos(theta)=1

Now just solve for the angles

Answer 2

thankyou!