Question

решите:
а) 1+sin a = 2cos²(45°- a/2)
b) 2sin²(45°- a) + sin 2a = 1
c) 1 - sin a = 2 sin²(45°- a/2)

Answer 1

а) 1+sin a = 2cos²(45°- a/2)
1+sina=2*(1+cos(90-a))/2=1+sina
1+sina=1+sina
формула cos²a=(1-cos2a)/2
b) 2sin²(45°- a) + sin 2a = 1
2(1-cos(90-2a))/2+sin2a=1-sin2a+sin2a=1
1=1
c) 1 - sin a = 2 sin²(45°- a/2)
1-sina=2(1-cosa)/2=1-sina
1-sina=1-sina