Question

Tentukan nilai dari [tex]\displaystyle \left ( 1+\cos \frac{\pi}{8} \right )\left ( 1+\cos \frac{3\pi}{8} \right )\left ( 1+\cos \frac{5\pi}{8} \right )\left ( 1+\cos \frac{7\pi}{8} \right )[/tex]

Answer 1

Penjelasan dengan langkah-langkah:

[tex]\tt (1+cos( \frac{\pi }{8}))(1+cos(\frac{3\pi}{8}))(1+cos(\frac{5\pi }{8})) (1+cos(\frac{7\pi}{8}))\\\\= (1+\sqrt{\frac{1+cos(\frac{\pi}{4})}{2}})(1+\sqrt{\frac{1+cos(\frac{3\pi}{4})}{2}})(1-\sqrt{\frac{1+cos(\frac{5\pi}{4})}{2}})(1-\sqrt{\frac{1+cos(\frac{7\pi }{4})}{2}})[/tex]

[tex]\tt = (1+\sqrt{\frac{1+\frac{\sqrt{2}}{2}}{2} } )(1+\sqrt{\frac{1-\frac{ \sqrt{2}}{2}}{2}}) (1-\sqrt{\frac{1-\frac{\sqrt{2}}{2}}{2}})(1-\sqrt{\frac{1+\frac{\sqrt{2}}{2}}{2}}) \\\\= (1+\sqrt{\frac{(2+\sqrt{2})}{2^2}})(1+\sqrt{\frac{\frac{2-\sqrt{2}}{2} }{2}})(1-\sqrt{\frac{(2-\sqrt{2})}{2^2}})(1-\sqrt{\frac{\frac{2+\sqrt{2} }{2} }{2}}) \\\\= (1+ \frac{\sqrt{2+\sqrt{2}} }{2} })(1+\sqrt{\frac{(2-\sqrt{2})}{2^2}})(1-\frac{\sqrt{2-\sqrt{2} }}{2})(1-\frac{\sqrt{2+\sqrt{2}}}{2})\\ \\= 0,125\\\\= 0[/tex]

Nilai dari [tex]\tt (1+cos( \frac{\pi }{8}))(1+cos(\frac{3\pi}{8}))(1+cos(\frac{5\pi }{8})) (1+cos(\frac{7\pi}{8}))[/tex] adalah 0