2/2 - 2cos(75)+2sin(75)
(√2+1)/2
Объяснение:
√2/2 - (cos^2 75° - 2 cos 75°sin 75° + sin^2 75°)=
= √2/2 - cos^2 75° + 2 cos 75°sin 75° - sin^2 75°
*2 cos 75°sin 75° = sin 2*75 = sin 150°
если cos^2 75° + sin^2 75° = 1, тогда
-cos^2 75° - sin^2 75° = -1
= √2/2 -1 +sin 150° = √2/2 - 1 + sin 150° = √2/2 -1 + sin ( 90°+60°) =
= √2/2 - 1 + (sin 90° cos 60°+ cos 90°sin 60°) = √2/2 + 1* 0.5 +0*0.86 =
= √2/2 +0.5 = √2/2+1/2 = = (√2+1)/2
