Question

Please help

Answer 1

\(\bf sec\left(\frac{x}{2}\right)=cos\left(\frac{x}{2}\right)\implies \cfrac{1}{cos\left(\frac{x}{2}\right)}=cos\left(\frac{x}{2}\right)\implies 1=cos^2\left(\frac{x}{2}\right)
\\ \quad \\
1-cos^2\left(\frac{x}{2}\right)=0\)

any ideas?

Answer 2

Sorry not really...am I supposed to get something on the side with 0?

Answer 3

\(\bf sec\left(\frac{x}{2}\right)=cos\left(\frac{x}{2}\right)\implies \cfrac{1}{cos\left(\frac{x}{2}\right)}=cos\left(\frac{x}{2}\right)\implies 1=cos^2\left(\frac{x}{2}\right)
\\ \quad \\
1-cos^2\left(\frac{x}{2}\right)=0
\\ \quad \\
{\color{brown}{ sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)}}\qquad thus
\\ \quad \\
1-cos^2\left(\frac{x}{2}\right)=0\implies sin^2\left(\frac{x}{2}\right)=0\quad \\ sin^{-1}\left[sin^2\left(\frac{x}{2}\right)\right]=sin^{-1}(0)\implies

\cfrac{x}{2}=sin^{-1}(0)
\\ \quad \\
\implies x=2\cdot [sin^{-1}(0)]\)

Answer 4

how does that convert to a fraction or fractions with pi?