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geografrussia
@geografrussia
August 2022
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Найти значение выражения:
sin^4a-cos^4a, если sina-cosa=0.7
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tseluyko58
Verified answer
Sin⁴L-cos⁴L=(sin²L+cos²L)*(sin²L-cos²L)=sin²L-cos²L=(sinL-cosL)*(sinL+cosL)=0,7*(sinL+cosL)
(sinL-cosL)²=1-2sinLcosL=0,49
2sinLcosL=1-0,49=0,51
(sinL+cosL)²=1+2sinLcosL=1+0,51=1,51
sinL+cosL=+-√1,51, отсюда
sin⁴L-cos⁴L=0,7*√1,51
sin⁴L-cos⁴L=-0,7*√1,51
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Answers & Comments
Verified answer
Sin⁴L-cos⁴L=(sin²L+cos²L)*(sin²L-cos²L)=sin²L-cos²L=(sinL-cosL)*(sinL+cosL)=0,7*(sinL+cosL)(sinL-cosL)²=1-2sinLcosL=0,49
2sinLcosL=1-0,49=0,51
(sinL+cosL)²=1+2sinLcosL=1+0,51=1,51
sinL+cosL=+-√1,51, отсюда
sin⁴L-cos⁴L=0,7*√1,51
sin⁴L-cos⁴L=-0,7*√1,51