Sin(-7п)-tg(7п/3) - корень из 3 cos(-7П/4)

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Let's simplify each trigonometric function step by step:

sin(-7π) = -sin(7π) = 0
(since sine function is periodic with period 2π, sin(7π) = sin(0) = 0)

tan(7π/3) = tan(2π + π/3) = tan(π/3) = √3
(since tangent function is periodic with period π, tan(2π) = tan(0) = 0 and tan(π/3) = √3)

cos(-7π/4) = cos(π/4) = √2/2
(since cosine function is periodic with period 2π, cos(7π/4) = cos(π/4))

Putting it all together:

-0 - √3 - √3 * √2/2
= -√3 - √6/2
= -√3 - √6/2
= -(√3 + √6)/2

Therefore, Sin(-7п) - tg(7п/3) - √3cos(-7П/4) simplifies to -(√3 + √6)/2.