1)sin^4a+ cos^4a= (1+ cos^2a)/(2) 2)ctga-tga=2ctg2a 3)1-tg^a/1+tg^2a=cos2a Доказать...

Question

1)sin^4a+ cos^4a= (1+ cos^2a)/(2)
2)ctga-tga=2ctg2a
3)1-tg^a/1+tg^2a=cos2a
Доказать тождество
Заранее благодарю.

Answer 1

1
sin^4a+cos^4a=(1-cos2a)²/4+(1+cos2a)²/4=
=1/4*(1-2cos2a+cos²2a+1+2cos2a+cos²2a)=1/4*(2+2cos²2a)=
=1/2*(1+cos²2a)
2
ctga-tga=cosa/sina-sina/cosa=(cos²a-sin²a(/(sinacosa)=cos2a:1/2*sin2a=
=2cos2a/sin2a=2ctg2a
3
(1-tg²a)/(1+tg²a)=(1-sin²a/cos²a):(1+sin²a/cos²a)=
=(cos²a-sin²a)/cos²a:(cos²a+sin²a)/cos²a=cos2a/cos²a*cos²a/1=cos2a

Comments

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