Корень 2/2 - ( cos 75 - sin 75)2

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