1)cos^2a+sin^2a+tg^2b 2)sin2a/2sina 3)sin a cos 3a - cos a sin 3a

1) cos^2(a) + sin^2(a) + tg^2(b) = 1/cos^2(b)
a)По основному тригонометрическому тождеству имеем: sin^2(a) + cos^2(a) = 1, тогда cos^2(a) + sin^2(a) = 1
b)1 + tg^2(b) = 1/cos^2(b)
2) sin(2a)/2sin(a) = cos(a)
а) sin(2a) = 2 * sin(a) * cos(a) 
b) sin(2a)/2sin(a) = 2 * sin(a) * cos(a)/2sin(a) = cos(a)
3) sin(a) * cos(3a) - cos(a) * sin(3a) = -2 * sin(a) * cos(a)
a) по формуле sin(a - b) = sin(a) * cos(b) - cos(a) * sin(b)
b) sin(a) * cos(3a) - cos(a) * sin(3a) = sin(a - 3a) = sin(-2a) = -sin(2a) = -2 * sin(a) * cos(a)
4)(1 - tg(x))^2 + (1 + tg(x))^2 = 1 - 2 * tg(x) + tg^2(x) + 1 + 2 * tg(x) + tg^2(x) = 1 + tg^2(x) + 1  + tg^2(x) = 2(1 + tg^2(x)) = 2 * 1/cos^2(x) = 2/cos^2(x)