Question

Упростите выражения:
а) (Cosa-Sina)^2-(Cosa+Sina)^2=
б)Sin^2a-tg^2a
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Cos^2a-Ctg^2a

Answer 1

а). (cosα-sinα)²-(cosα+sinα)²=cos²α-2cosα*sinα+sin²α-(cos²α+2coα*sinα+sin²α)=-2*2sinα*cosα=-2sin2α
б). (sin²α-tg²α)/(cos²α-ctg²α)=(sin²α- sin²α/cos²α)/(cos²α- cos²α/sin²α)=
 =[ (sin²α*cos²α-sin²α)/cos²α] / [ (cos²α*sin²α-cos²α)/sin²α ]=
[ (sin²α(cos²α-1)/cos²α ]/ [ cos²α(sin²α-1)/sin²α ]=
= [ sin²α*(-sin²α)/cos²α ] / [ cos²α*(-cos²α)/sin²α ] =sin⁶α/ cos⁶α=tg⁶α