Hitunglah nilai eksak dari 1/2-sin^2 15

Hitunglah nilai eksak dari 1/2-sin^2 15

Jawaban Terkonfirmasi

$frac{1}{2}-sin^2(15)=frac{1}{2}-(sin(15))^2\\ =frac{1}{2}-(sin(45-30))^2\\ =frac{1}{2}-(sin(45)cos(30)-cos(45)sin(30))^2\\ =frac{1}{2}-((frac{1}{2}sqrt{2})(frac{1}{2}sqrt{3})-(frac{1}{2}sqrt{2})(frac{1}{2}))^2\\ =frac{1}{2}-(frac{1}{4}sqrt{6}-frac{1}{4}sqrt{2})^2\\ =frac{1}{2}-(frac{6}{16}-frac{1}{16}sqrt{12}-frac{2}{16})\\ =frac{1}{2}-(frac{4}{16}-frac{1}{16}sqrt{12})\\ =frac{1}{2}-(frac{1}{4}-frac{1}{16}sqrt{12})\$
$=frac{1}{2}-frac{1}{4}+frac{1}{16}sqrt{12}\\ =frac{1}{4}+frac{1}{16}sqrt{12}\$