Question

cos^2(45/2)+cos^2(135/2)+cos^2(225/2)+cos^2(315/2)=

Answer 1

Answer:

Step-by-step explanation:

Given Cos^2(45/2)+cos^2(135/2)+cos^2(225/2)+cos^2(315/2)

So 1/2 (cos^2 45 + cos^2 135 + cos^2 225 + cos^2 315)

 1/2 (cos^245 + (cos(90 + 45))^2 + (cos(180 + 45)^2 + cos (270 + 45)^2

 1/2 (cos^2 45 + (- sin 45)^2 + (- cos 45)^2 + (sin 45)^2

 1/2 ( cos^2 45 + sin^2 45 + cos^2 45 + sin^2 45)

 1/2 ( 1 + 1) ( because cos^2 45 + sin^2 45 = 1)

 1/2 x 2

= 1