Question

Trigonometric Identities and Applications?

Answer 1

21)

$\bf 8cos^2(\theta )-3cos(\theta )=0\implies \stackrel{common~factor}{cos(\theta )}[8cos(\theta )-3]=0\\\\ -------------------------------\\\\ cos(\theta )=0\implies \measuredangle \theta =cos^{-1}(0)\implies \measuredangle \theta =90^o\\\\ -------------------------------\\\\ 8cos(\theta )-3=0\implies 8cos(\theta )=3\implies cos(\theta )=\cfrac{3}{8} \\\\\\ \measuredangle \theta =cos^{-1}\left( \cfrac{3}{8}\right)$

22)

$\bf \begin{cases} y=cos(2x)\\ y=cos^2(x)-1 \end{cases}\implies \stackrel{intersection~at}{cos(2x)=cos^2(x)-1} \\\\\\ 2cos^2(x)-1=cos^2(x)-1\implies 2cos^2(x)-1-cos^2(x)+1=0 \\\\\\ 2cos^2(x)-cos^2(x)=0\implies cos^2(x)=0\implies cos(x)=0 \\\\\\ \measuredangle \theta =cos^{-1}(0)\implies \measuredangle \theta =180^o~~,~~270^o$