Arcsin(ctg(π/4))=arcsin(1)=π/2
cos(arcsin(-1/2)-arcsin(1))=cos(2π/3-π/2)=cos(4π/6-3π/6)=cos(π/6)=√3/2
<h3>(3X-11)/4-(3-5X)/8= (X+6)/2</h3><h3>2(3X-11)-(3+5X)=4(X+6)</h3><h3>6X-22-3+5X=4X+24</h3><h3>7X=24+22+3</h3><h3>7X=49</h3><h3>X=7</h3><h3 /><h3 />
Обозначим
arcsin 3/5=α, тогда sin α=3/5, 0≤α≤π/2
найдем cos α=√1 - (3/5)²=√1- 9/25=√16/25=4/5 и tg α=sin α/cos α=3/4
arccos 1/4=β, cos β=1/4 b 0≤β≤π/2
sin β=√1-(1/4)²=√15/4 и tg β=√15
tg(arcsin 3/5-arccos 1/4)=tg(α-β)=(tg α - tgβ)/1+tgα·tgβ=(3/4-√15)/1+3√15/4 =
=(3-4√15)/(4+3√15)