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LiraReimand
@LiraReimand
September 2021
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Помогите упростить,ничего из новой темы не пойму, пожалуйста ) только 129
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sangers1959
Verified answer
1) 2*cos40°*cos50°=2*cos50°*cos40°=2*((cos(50°-40°)+cos(50°+40°))/2=
=cos10°+cos90°=cos10°.
2) 2*sin25°*sin65°=sin65°*sin25°=2*((cos(65°-25°)-cos(65°+45°))/2=
=cos40°-cos90°=cos40°.
3) sin2α+(sinα-cosα)²=2sinαcosα+sin²α-2sinαcosα+cos²α=sin²α+cos²α=1.
4) cos4α+sin²2α=cos²2α-sin²2α+sin²2α=cos²2α.
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Answers & Comments
Verified answer
1) 2*cos40°*cos50°=2*cos50°*cos40°=2*((cos(50°-40°)+cos(50°+40°))/2==cos10°+cos90°=cos10°.
2) 2*sin25°*sin65°=sin65°*sin25°=2*((cos(65°-25°)-cos(65°+45°))/2=
=cos40°-cos90°=cos40°.
3) sin2α+(sinα-cosα)²=2sinαcosα+sin²α-2sinαcosα+cos²α=sin²α+cos²α=1.
4) cos4α+sin²2α=cos²2α-sin²2α+sin²2α=cos²2α.