( 24^3 ) / ( 18^4 ) = ( 6^3•4^3 ) / ( 6^4•3^4 ) = ( 4^3 ) / ( 6•3^4 ) = ( 2^6 )/ ( 2•3^5 ) = ( 2^5 ) / ( 3^5 ) = ( 2/3 )^5
3б)
Делим на cos²x≠0
3tg²x+2√3tgx+1=0
D=(2√3)²-4·3=12-12=0
tgx=-2√3/6;
tgx=-√3/3
x=(-π/6)+πk, k∈Z
О т в е т. (-π/6)+πk, k∈Z
5a)
делим на (1/√2)
(1/√2)sinx+(1/√2)cosx=(1/√2)
1/√2=sinπ/4=cosπ/4
(cos(π/4))sinx+(sin(π/4))cosx=1/√2
sin(x+π/4)=1/√2
x+(π/4)=π/4+2πk, k∈Z или х+(π/4)=3π/4+2πn, n∈Z
x=2πk, k∈Z или х=(π/2)+2πn, n∈Z
О т в е т.2πk; (π/2)+2πn; k, n∈Z
5б)
sin4x=2sin2x·cos2x
2cos²x=1+cos2x
1+cos2x+2sin2xcos2x=1
cos2x(1+2sin2x)=0
cos2x=0 или sin2x=-1/2
2x=(π/2)+πk, k∈Z<span>; 2x= </span>(-π/6)+2πn, n∈<span>Z или 2х=</span>(-5π/6)+2πm, m∈Z
x=(π/4)+(π/2)·k, k∈Z; x= (-π/12)+πn, n∈Z или х=(-5π/12)+πm, m∈Z
О т в е т.(π/4)+(π/2)·k; (-π/12)+πn; (-5π/12)+πm; k, n, m∈Z
[(x+y)/2-(x-y)/2]*[(x+y)/2+(x-y)/2]=(x+y-x+y)/2*(x+y+x-y)/2=2y/2*2x/2=xy
xy=xy
= A - ( 2B - ( 2A - 2D - 2A )) = A - ( 2B + 2D ) = A - 2B - 2D