Question

Вычислить cos 13п/24 * сos 7п/24

Answer 1

$cos alpha *cos beta = frac{1}{2}(cos( alpha + beta )+cos( alpha - beta )) \ cos frac{13 pi }{24} *cos frac{7 pi }{24}= frac{1}{2}(cos frac{13 pi +7 pi }{24}+cos frac{13 pi -7 pi }{24})= \ = frac{1}{2}(cos frac{20 pi }{24}+cos frac{6 pi }{24})= frac{1}{2}(cos frac{5 pi }{6}+cos frac{ pi }{4})= \ = frac{1}{2}( -frac{ sqrt{3} }{2} + frac{ sqrt{2} }{2})= frac{ sqrt{2}- sqrt{3}}{4}$