Question

Найти значение выражений: 1)5•корень из 2•sin11pi/8•cos11pi/8; 2)корень из 48•cos^2(7pi/12)-корень из 48•sin^2(7pi/12);

Answer 1

1) $5 \sqrt{2}sin \frac{11 \pi }{8} cos\frac{11 \pi }{8} = \frac{5 \sqrt{2}}{2} sin(2* \frac{11 \pi }{8} )= \frac{5 \sqrt{2}}{2} sin \frac{11 \pi }{4} = \frac{5 \sqrt{2}}{2} sin \frac{3 \pi }{4} =\\ = \frac{5 \sqrt{2}}{2} * \frac{ \sqrt{2} }{2} =2,5$

2) $\sqrt{48} cos^2 \frac{7 \pi }{12} - \sqrt{48} sin^2 \frac{7 \pi }{12} = \sqrt{48} (cos^2 \frac{7 \pi }{12} - sin^2 \frac{7 \pi }{12}) =\\ = \sqrt{48} (cos(2* \frac{7 \pi }{12})=\sqrt{48} cos \frac{7 \pi }{6}= 4\sqrt{3} *(- \frac{ \sqrt{3} }{2})=-6$

Answer 2

5√2sin11π/8*cos11π/8=5√2*1/2*sin11π/4=5√2/2*sin(3π-π/4)=
=5√2/2*sinπ/4=5√2/2*1/√2=5/2=2,5

√48cos²7π/12-√48sin²7π/12=4√3(cos²7π/12-sin²7π/12)=4√3*cos7π/6=
=4√3*cos(π+π/6)=-4√3cosπ/6=-4√3*√3/2=-6