Докажите тождество:

sina + cosa - sin (a - π/6) + cos (a - π/6) = √6cos (a - π/12)

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Алгебра

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9 ноября, 06:21

Докажите тождество:

sina + cosa - sin (a - π/6) + cos (a - π/6) = √6cos (a - π/12)

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Петаня · Answer 1

2sinπ/12cos (a-π/12) + 2cosπ/12cos (a-π/12) =

=2cos (a-π/12) * (sinπ/12+cosπ/12) = 2cos (a-π/12) (sinπ/12+sin5π/12) =

=2cos (a-π/12) * 2sinπ/4cosπ/6=4*√2/2*√3/2cos (a-π/12) = √6cos (a-π/12)

Докажите тождество:sina + cosa - sin (a - π/6) + cos (a - π/6) = √6cos (a - π/12)

Докажите тождество:

sina + cosa - sin (a - π/6) + cos (a - π/6) = √6cos (a - π/12)