Question

(cos^2(37)-sin^2(23))/sin104

Решите пожалуйста

Answer 1

$frac{cos^2 37^{circ} - sin^2 23^{circ}}{sin 104^{circ}} = frac{cos^2 37^{circ} - sin^2 23^{circ}}{sin 104^{circ}} = frac{(cos 37^{circ} - sin 23^{circ})(cos 37^{circ} + sin 23^{circ})}{sin 104^{circ}} = \\ = frac{(sin 53^{circ} - sin 23^{circ})(sin 53^{circ} + sin 23^{circ})}{sin 104^{circ}} = frac{2sin 15^{circ}cos 38^{circ}*2sin38^{circ}cos 15^{circ}}{2sin 52^{circ}cos 52^{circ}} =$

$= frac{4sin 15^{circ}cos 15^{circ}cos 38^{circ}sin38^{circ}}{2sin(90^{circ} - 38^{circ})cos(90^{circ} - 38^{circ})} = frac{4sin 15^{circ}cos 15^{circ}cos 38^{circ}sin38^{circ}}{2cos 38^{circ}sin38^{circ}} = \\ = 2sin 15^{circ}cos 15^{circ} = sin 30^{circ} = frac{1}{2}$

$boxed{ sin a pm sin b = 2sin frac{a pm b}{2}cosfrac{a mp b}{2} }$