Cos^4 23 П/12 - sin^4 13 П/12

Question

Алгебра

Нинуля

5 марта, 14:11

Cos^4 23 П/12 - sin^4 13 П/12

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Онуфрий · 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