Cos^22a - sin(p/3-2a)cos(2a - p/6) =1/4 ctga=2/3 0 найти: cos(a+7p/4) 1+cos2a+sin2a/sina+cosa y=ctgx/3

Cos^22a-cos(П/6+2a)cos(П/6-2a)=1/4
cos^2a-1/2[1/2+cos4a]=1/4
cos^22a-cos^22a+sin^22a=1/2
sin2a=√2/2
sin2a=-√2/2
a=1/2*(-1)^k+Пk/2
a=1/2)-1)^k+1+Пk/2
cos(a+2П-П/4)=cos(a-П/4)=cosacosП/4+sinasinП/4=√2/2(cosa+sina)=3√2/2√13(2/3+1)=
=5√2/2√13
cosa/sina=2/3
(1-sin^2a)/sin^2a=4/9
9=13sin^2a
sina=3/√13
(cosa+sina)(cosa+sina+cosa-sina)/(cosa+sina)=2cosa