Question

Trigonometric Identities question: http://d.pr/i/FsnP

I got my answer to be 3/2 but the mark scheme says -3/2.

Answer 1

\[3\cos2 \beta+19\cos \beta+13=0\]
\[Use ~~~~\cos2\beta=2\cos^2\beta-1\]
\[3(2\cos^2\beta-1)+19\cos \beta+13=0\]
\[6\cos^2\beta-3+19\cos \beta+13=0\]
\[6\cos^2\beta+19\cos \beta+10=0\]
\[(2\cos \beta+5)(3\cos \beta+2)=0\]
\[\cos \beta=-5/2, \cos \beta =-2/3\]

Answer 2

Thanks. I made a silly mistake.