1 Ответ a 2 Ответ б 3 у=cosx/5 k=1/5 T=2π/k=2π;1/5=2π*5=10π Ответ б 4 cosa=-0,8 sina=-√(1-cos²a)=-√(1-0,64)=-√0,36=-0,6 tga=sina/cosa=-0,6:(-0,8)=3/4 5 a)sinπ/36cosπ/18+sinπ/18cosπ/36=sin(π/36+π/18)=sin3π/36=sinπ/12 b)2tg15/(1-tg²15)=tg(2*15)=tg30=√3/3 6 (cosa+cos7a)/(sina+sin7a)=2cos4acos3a/2sin4acos3a=ctg4a ctg4a=ctg4a 7 2cos²3xcosx-sinxsin6x=2cos²3xcosx-2sin3xcos3xsinx=2cos3x(cos3xcosx-sin3xsinx)=2cos3x*cos(3x+x)=2cos3xcos4x 8 sinx+cosx=t (sinx+cosx)²=1+2sinxcosx sinxcosx=0,5(sinx+cosx)²-0,5=0,5t²-0,5 sin³x+cos³x=(sinx+cosx)(sin²x-sinxcosx+cos²x)=(sinx+cosx)(1-sinxcosx)= =t*(1-0,5t²+0,5)=t(1,5-0,5t²)
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1Ответ a
2
Ответ б
3
у=cosx/5
k=1/5 T=2π/k=2π;1/5=2π*5=10π
Ответ б
4
cosa=-0,8
sina=-√(1-cos²a)=-√(1-0,64)=-√0,36=-0,6
tga=sina/cosa=-0,6:(-0,8)=3/4
5
a)sinπ/36cosπ/18+sinπ/18cosπ/36=sin(π/36+π/18)=sin3π/36=sinπ/12
b)2tg15/(1-tg²15)=tg(2*15)=tg30=√3/3
6
(cosa+cos7a)/(sina+sin7a)=2cos4acos3a/2sin4acos3a=ctg4a
ctg4a=ctg4a
7
2cos²3xcosx-sinxsin6x=2cos²3xcosx-2sin3xcos3xsinx=2cos3x(cos3xcosx-sin3xsinx)=2cos3x*cos(3x+x)=2cos3xcos4x
8
sinx+cosx=t
(sinx+cosx)²=1+2sinxcosx
sinxcosx=0,5(sinx+cosx)²-0,5=0,5t²-0,5
sin³x+cos³x=(sinx+cosx)(sin²x-sinxcosx+cos²x)=(sinx+cosx)(1-sinxcosx)=
=t*(1-0,5t²+0,5)=t(1,5-0,5t²)