Question

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А) 2cos13*cos43-cos56/2sin58cos13-sin71

Б) 2cos10*cos70-cos80/2sin40cos10-sin50

Answer 1

1)2cos13cos43-cos(13+43)=2cos13cos43-cos13cos43+sin13sin43=
=cos13cos43+sin13sin43=cos(43-13)=cos30=√3/2
2sin58cos13-sin(58+13)=2sin58cos13-sin58cos13-cos13sin58=
=sin58cos13-cos13sin58=sin(58-13)=sin45=√2/2
(2cos13*cos43-cos56)/(2sin58cos13-sin71)=√3/2:√2/2=√3/2*2/√2=√3/√2=√6/2
2)2cos10cos70-cos(10+70)=2cos10cos70-cos10cos70+sin10sin70=
=cos10cos70+sin10sin70=cos(70-10)=cos60=1/2
2sin40cos10-sin(40+10)=2sin40cos10-sin40cos10-cos40sin10=
=sin40cos10-cos10sin40=sin(40-10)=sin30=1/2
(2cos10*cos70-cos80)/(2sin40cos10-sin50)=1/2:1/2=1