Упрощение тригонометрических выражений. Задача 58math100admin44242025-03-24T16:41:00+03:00
Задача 58. Вычислите \(\dfrac{{\sin {{24}^ \circ }\cos {6^ \circ }-\sin {6^ \circ }\sin {{66}^ \circ }}}{{\sin {{21}^ \circ }\cos {{39}^ \circ }-\sin {{39}^ \circ }\cos {{21}^ \circ }}}\)
Решение
\(\dfrac{{\sin {{24}^ \circ }\cos {6^ \circ }-\sin {6^ \circ }\sin {{66}^ \circ }}}{{\sin {{21}^ \circ }\cos {{39}^ \circ }-\sin {{39}^ \circ }\cos {{21}^ \circ }}} = \dfrac{{\sin {{24}^ \circ }\cos {6^ \circ }-\sin {6^ \circ }\cos {{24}^ \circ }}}{{\sin {{21}^ \circ }\cos {{39}^ \circ }-\sin {{39}^ \circ }\cos {{21}^ \circ }}} = \)
\( = \dfrac{{\sin \left( {{{24}^ \circ }-{6^ \circ }} \right)}}{{\sin \left( {{{21}^ \circ }-{{39}^ \circ }} \right)}} = \dfrac{{\sin {{18}^ \circ }}}{{\sin \left( {-{{18}^ \circ }} \right)}} = \dfrac{{\sin {{18}^ \circ }}}{{-\sin {{18}^ \circ }}} = -1.\)
Ответ: \(-1.\)