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shynar025
@shynar025
August 2022
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24 и 25 примеры по тригонометрии
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sedinalana
24
(ctg²2a-1)/2ctg2a -cos8a*ctg4a=ctg4a-cos8a*ctg4a=
=ctg4a*(1-cos8a)=cos4a/sin4a *2sin²4a=2sin4a8cos4a=sin8a
25
(sin^4a-cos^4a+cos²a)/2(1-cosa)=
=[(sin²a+cos²a)(sin²a-cos²a)+cos²a]/2(1-cosa)=
=(sin²a-cos²a+cos²a)/2(1-cosa)=sin²a/2(1-cosa)=
(1-cos²a)/2(1-cosa)=(1-cosa)(1+cosa)/2(1-cosa)=(1+cosa)/2=
=2cos²(a/2)/2=cos²(a/2)
1 votes
Thanks 3
shynar025
Спасибо!
shynar025
А в первом примере откуда в конце 8 вышло?
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Answers & Comments
(ctg²2a-1)/2ctg2a -cos8a*ctg4a=ctg4a-cos8a*ctg4a=
=ctg4a*(1-cos8a)=cos4a/sin4a *2sin²4a=2sin4a8cos4a=sin8a
25
(sin^4a-cos^4a+cos²a)/2(1-cosa)=
=[(sin²a+cos²a)(sin²a-cos²a)+cos²a]/2(1-cosa)=
=(sin²a-cos²a+cos²a)/2(1-cosa)=sin²a/2(1-cosa)=
(1-cos²a)/2(1-cosa)=(1-cosa)(1+cosa)/2(1-cosa)=(1+cosa)/2=
=2cos²(a/2)/2=cos²(a/2)