Question

9 класс
вычислить: cos240градусов
cos98cos53+sin98sin93=
sin56cos26-cos56sin26=
$sin \frac{8 \pi }{7}cos \frac{6 \pi }{7}+sin \frac{6 \pi }{7}cos \frac{8 \pi }{7}=$
Упростить:
$\frac{1+sin( \pi + \alpha) }{1-cos( \frac{3 \pi }{2}+ \alpha ) } = \frac{cos^{2}( \pi + \alpha ) }{1-cos( \frac{3 \pi }{2}+ \alpha ) }$

Answer 1

cos240=cos(180+60)=-cos60=-1/2

cos98*cos53+sin53*cos98=cos(98-53)=cos45=√2/2

sin56*cos56-cos56*sin26=sin(56-26)sin30=1/2

sin(8π/7)*cos(6π/7)+sin(6π/7)*cos(8π/7)=sin(8π/7+6π/7)=sin2π=0

(1+sin(π+α))/(1-cos(3π/2+α))=cos²(π+α)/(1-cos3π/2+α))
1+sin(π+α)=cos²(π+α)
1-sinα=cos²α
sin²α+cos²α-sinα-cos²α=sin²α-sinα