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Infinity8881
@Infinity8881
August 2021
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Упростить:
cos^3(pi/12) + sin^3(pi/12)
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Verified answer
Cos^3(pi/12) + sin^3(pi/12)=
(cos(pi/12) + sin(pi/12)) (cos^2(pi/12) -cos(pi/12) sin(pi/12) +sin^2(pi/12))=
=(cos(pi/12) + sin(pi/12)) (1-1/2sin(pi/6)=(√((cos(pi/12) + sin(pi/12))
^2) 3/4=
=3/4[
√(1+2cos(pi/12) sin(pi/12)]=3/4 [√(1+ sin(pi/6))]=3/4[√(1+1/2)]=3/4[
√(3/2)]
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Answers & Comments
Verified answer
Cos^3(pi/12) + sin^3(pi/12)=(cos(pi/12) + sin(pi/12)) (cos^2(pi/12) -cos(pi/12) sin(pi/12) +sin^2(pi/12))=
=(cos(pi/12) + sin(pi/12)) (1-1/2sin(pi/6)=(√((cos(pi/12) + sin(pi/12))^2) 3/4=
=3/4[√(1+2cos(pi/12) sin(pi/12)]=3/4 [√(1+ sin(pi/6))]=3/4[√(1+1/2)]=3/4[√(3/2)]