[ log₀,₃(x+1)/(log₀,₃100-log₀,₃9) ] <1<br>[ log₀,₃(x+1)/(log₀,₃100-log₀,₃9) -1]<0<br>
[ log₀,₃(x+1)-log₀,₃100+log₀,₃9] /(log₀,₃100-log₀,₃9)<0<br>[ log₀,₃(x+1)+log₀,₃0,09 ] / [-log₀,₃0,09]<0 |*(-1)<br>[ log₀,₃(x+1)+log₀,₃0,09 ] / 2>0
{log₀,₃(x+1)+log₀,₃0,09>0
2>0
log₀,₃(x+1)+log₀,₃0,09>0
log₀,₃(x+1)>-log₀,₃0,09
log₀,₃(x+1)>log₀,₃0,09⁻¹ 0,09⁻¹=(9/100)⁻¹=100/9
0<0,3<1 знак неравенства меняем<br>
{x+1<(100/9) {x<(91/9)<br>x+1>0 x>-1
x∈(-1;91/9)
наибольшее целое решение х=10
cosα=-(1/3), sinα=?
sin²α+cosα=1
sin²α+(-1/3)²=1, sin²α=8/9
sinα=+-√(8/9), π<α<3π/2. ⇒<br>sinα=-√(8/9)
sinα=-2√2/3
sin135°+cos210°-sin(-150°)+cos225°=sin(90°+45°)+cos(180°-30°)+sin(180°-30°)+cos(180°+45°)=cos45-cos30°+sin30°-cos45°=sin30°-cos30°=1/2-√3/2=(1-√3)/2