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Espressione trigonometria

Analizziamo separatamente i due addendi:

SIN(2·α - pi/6)=

=SIN(2·α)·COS(pi/6) - SIN(pi/6)·COS(2·α)=

=SIN(2·α)·(√3/2) - 1/2·COS(2·α)=

=2·SIN(α)·COS(α)·√3/2 - 1/2·(COS(α)^2 - SIN(α)^2)=

=√3·SIN(α)·COS(α) - 1/2·(COS(α)^2 - SIN(α)^2)=

=√3·SIN(α)·COS(α) - 1/2·(2·COS(α)^2 - 1)=

=√3·SIN(α)·COS(α) - (COS(α)^2 - 1/2)

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2·COS(pi/3 + α)^2=

=2·(COS(pi/3)·COS(α) - SIN(pi/3)·SIN(α))^2=

=2·(1/2·COS(α) - √3/2·SIN(α))^2=

=2·((1/2·COS(α))^2 - √3/2·SIN(α)·COS(α) + (√3/2·SIN(α))^2)=

=2·(COS(α)^2/4 - √3/2·SIN(α)·COS(α) + 3·SIN(α)^2/4)=

=- √3·SIN(α)·COS(α) + SIN(α)^2 + 1/2

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sommiamo i due termini:

√3·SIN(α)·COS(α) - (COS(α)^2 - 1/2) +

+(- √3·SIN(α)·COS(α) + SIN(α)^2 + 1/2)=

=- COS(α)^2 + 1/2 + SIN(α)^2 + 1/2=

=- COS(α)^2 + SIN(α)^2 + (SIN(α)^2 + COS(α)^2)=

= 2·SIN(α)^2