Question

Sin54*sin24-sin66*cos126

Answer 1

Объяснение:

по формулам привидения:

$sin {24}^{0} = sin( {90}^{0} - {66}^{0} ) = cos {66}^{0}$

$cos {126}^{0} = cos( {180}^{0} - {54}^{0} ) = - sin {54}^{0}$

$sin {54}^{0} sin {24}^{0} - sin {66}^{0} cos {126}^{0} = \\ sin {54}^{0} cos {66}^{0} - sin {66}^{0} ( - cos {54}^{0}) = \\ sin {54}^{0} cos {66}^{0} + sin {66}^{0} cos {54}^{0} = \\ cos( {54}^{0} - {66}^{0} ) = \\ cos( - {12}^{0} ) = cos {12}^{0}$