Question

Show that cos2(45-A)+cos2(45+A)=1

Answer 1

cos²(45°—A) + cos²(45°+A)
= [2 cos²(45°—A) + 2 cos²(45°+A)] /2
= [{2 cos²(45°—A)—1} + {2 cos²(45°+A)—1} + 2] /2
= [cos2(45°—A)+cos2(45°+A)+2]/2
= [cos(90°—2A)+cos(90°+2A)+2]/2
= (sin2A—sin2A+2)/2
= 2/2
= 1

Answer 2

Answer:

=Cos²(45°+A)+Cos²(45°-A)

={2Cos²(45° + A ) +2 Cos²( 45°-A)}/2

= { Cos2(45°+A) +1 + Cos2( 45°-A)}/2

={ Cos ( 90°+2A)+ 1 + Cos(90°-2A) }/2

={ -Sin2A +1 + Sin2A+1}/2

={1+1}/2

=2/2

=1

=RHS