Question

Помогите, пожалуйста, решить.

Answer 1

1) $39 sqrt{2}*tg( frac{pi}{4} )*sin( frac{pi}{4} )= 39 sqrt{2}* frac{sin( frac{pi}{4})}{cos(frac{pi}{4})} * frac{ sqrt{2} }{2} =$

$=39 sqrt{2}* frac{ frac{ sqrt{2} }{2} }{ frac{ sqrt{2} }{2} } * frac{ sqrt{2} }{2} =39 sqrt{2}*1*frac{ sqrt{2} }{2} =frac{39* (sqrt{2})^2 }{2} = frac{39*2}{2} =39$

2) $frac{48}{sin(- frac{19pi}{3} )cos( frac{25pi}{6} )} = frac{48}{-sin(frac{3*3*2pi+pi}{3} )cos( frac{2*6*2pi+pi}{6} )} =$

$=- frac{48}{sin(3*2pi+frac{pi}{3} )cos( 2*2pi+frac{pi}{6} )} =- frac{48}{sin(frac{pi}{3} )cos(frac{pi}{6} )} =- frac{48}{ frac{ sqrt{3} }{2} *frac{ sqrt{3} }{2} }=$

$=- frac{48}{ frac{3}{4} }=- frac{48*4}{3} =- frac{3*16*4}{3}=-16*4 -64$

3) $42 sqrt{3}*sin(120^0)=42 sqrt{3} *sin( frac{pi}{2}+ frac{pi}{6} )=42 sqrt{3}*cos( frac{pi}{6} )=$

$=42 sqrt{3}* frac{ sqrt{3} }{2}=21*3=63$