А) <span>√82 ² -18² = 82-324 = -242
б) </span><span>√113²-112² = 113-12544= -12431</span>
A = pi/4;
cos a = cos(pi/4)= sgrt2/2;
tg a = sin a / cos a = 1;
ctga = 1/tg a = 1;
3 tg(pi/4) + 2 tg^2(pi/4) - sgrt2*(sgrt2/2)= 3*1 +2*1 - 2/2=
= 3+2-1=4
1+ctg^2a=1/sin^2a
ctga=5/12 tga=1/ctga
tga=12/5 т.к <span>П<a<3П/2</span>
tg(<span>П</span>/4-a)=(tg<span>П</span>/4-tga)/1+tg<span>П</span>/4*tga)=(1-12/5)(1+12/5)=-7/17
<span>cos(П/4+t)cos(П/4-t)=1/2(cos(П/4+t-(П/4-t))+cos(П/4+t+П/4-t)=1/2(cos2t+cosП/2)=1/2cos2t=(2cos^2t-1)/2</span>
cos(П/4+t)+cos(П/4-t)=2cos((П/4+t-П/4+t)/2)*cos((П/4+t+П/4-t)/2)=2cost*cosП/4=√2cost=p
<span><span><span>cost=p/<span>√2</span></span></span></span>
<span><span><span><span><span>cos(П/4+t)cos(П/4-t)=(2cos^2t-1)/2=p^2-1</span></span></span></span></span>
<span><span><span> </span></span></span>