Cos^4 23П/12 - sin^4 13П/12

Question

Cos^4 23П/12 - sin^4 13П/12

Answer 1

[cos(2π-π/12)]^4 - [sin(π+π/12)]^4 = (cosπ/12)^4 -(-sinπ/12)^4 = 
    = (√(1+cosπ/6)/2)^4 - (√(1-cosπ/6)^4 =  (1+√3/2)²/16 - (1-√3/2)²/16=
  = 1/16 ·(1+√3/2+1-√3/2)(1+√3/2-1+√3/2) = 
  =1/16· 2·√3 =  √3/8