The biographies of Andrei Sakharov and Winston Churchill art mixed up here. Separata the biographies and write them down (See Ex. 42-44 on p. 18, Student's Book.)

 cos(pi/4-a)=cospi/4*cosa-sinpi/4*sina=v2/2cosa-v2/2sina=v2/2(-v7/4+3/4)

cos^2a+sin^2a=1  cos^2a=1-9/16=7/16  cosa=-v7/4
2)ctg2a=cos2a/sin2a=7/25/(-24/25)=-7/25
cosa=-4/5  sin^2a=1-16/25=9/25  sina=3/5   
sin2a=2sinacosa=2*3/5*(-4/5)=-24/25   cos2a=1-2sin^2a=1-2*9/25=7/25
3) sin2a-sin6a+cos4a=-2sin2acos4a+cos4a=cos4a(-2sin2a+1)
sin2a-sin6a=2sin(2a-6a/2)*cos(2a+6a/2)=2sin(-2a)cos4a=-2sin2acos4a
дальше не могу разобрать твои каракули