21)
[tex]\bf 8cos^2(\theta )-3cos(\theta )=0\implies \stackrel{common~factor}{cos(\theta )}[8cos(\theta )-3]=0\\\\
-------------------------------\\\\
cos(\theta )=0\implies \measuredangle \theta =cos^{-1}(0)\implies \measuredangle \theta =90^o\\\\
-------------------------------\\\\
8cos(\theta )-3=0\implies 8cos(\theta )=3\implies cos(\theta )=\cfrac{3}{8}
\\\\\\
\measuredangle \theta =cos^{-1}\left( \cfrac{3}{8}\right)[/tex]
22)
[tex]\bf \begin{cases}
y=cos(2x)\\
y=cos^2(x)-1
\end{cases}\implies \stackrel{intersection~at}{cos(2x)=cos^2(x)-1}
\\\\\\
2cos^2(x)-1=cos^2(x)-1\implies 2cos^2(x)-1-cos^2(x)+1=0
\\\\\\
2cos^2(x)-cos^2(x)=0\implies cos^2(x)=0\implies cos(x)=0
\\\\\\
\measuredangle \theta =cos^{-1}(0)\implies \measuredangle \theta =180^o~~,~~270^o[/tex]
