Cos^4 15pi/12-sin^4 5pi/12 Срочно)

Question

Cos^4 15pi/12-sin^4 5pi/12 Срочно)

Answer 1

Сos^4(5π/4)-sin^4(5π/12)=cos^4(π+π/4)-sin^4(π/2-π/12)=
=cos^4(π/4)-cos^4(π/12)=(1/√2)^4-(1+cos(π/6))²/4=
=1/4-(1+√3/2)²/4=1/4*(1-(1-√3/2)²)=1/4(1-1+√3-3/4)=
=1/4*(√3+3/4)=√3/4-3/16