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Solomina2
@Solomina2
July 2022
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Тригонометрия: упростите выражение. С решением.
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sedinalana
1+cos²a+(1+cos2a)/2=(2+2cos²a+1+cos2a)/2=(2cos²a+cos2a+3)/
=(2cos²a+2cos²a-1+3)/2=(4cos²a+2)/2=2cos²a+1
3cos²a+(1-cos2a)/2=(6cos²a+1-cos2a)/2=(6cos²a+1-2cos²a+1)/2=
=(4cos²a+2)/2=2cos²a+1
(2cos²a+1)/(2cos²a+1)=1
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Solomina2
А почему cos^4(a) = (1 + cos2a)/2 и sin^4(a) = (1-sin2a)/2,
Solomina2
sin^4(a) = (1-cos2a)/2 *, если (1+cos2a)/2 = cos²a, а (1-cos2a)/2 = sin²a
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Answers & Comments
=(2cos²a+2cos²a-1+3)/2=(4cos²a+2)/2=2cos²a+1
3cos²a+(1-cos2a)/2=(6cos²a+1-cos2a)/2=(6cos²a+1-2cos²a+1)/2=
=(4cos²a+2)/2=2cos²a+1
(2cos²a+1)/(2cos²a+1)=1