To simplify the given expression, we first need to find the values of the trigonometric functions at the given angles.
Find the value of ctg(5π/6)ctg(5π/6) = 1/tg(5π/6tg(5π/6) = tg(π - π/6) = -tg(π/6) = -√Therefore, ctg(5π/6) = 1/(-√3) = -1/√3 = -√3/3
Find the value of tg(π/12)tg(π/12) = sin(π/12) / cos(π/12)
We know the values of sin(π/12) and cos(π/12) are not easily simplified and therefore we will leave it as tg(π/12).
Find the value of ctg(π/12)ctg(π/12) = 1/tg(π/12)
Find the value of tg(7π/4)tg(7π/4) = tg(π + 3π/4) = tg(3π/4) = -1
Now putting all the values back into the original expression√3 (-√3/3) + tg(π/12) 1/ tg(π/12) + 2 * (-1) + = -3 + 1 + (-2) + = -3 + 1 - 2 + = -4
Therefore, the simplified value of the expression is -4.
To simplify the given expression, we first need to find the values of the trigonometric functions at the given angles.
Find the value of ctg(5π/6)
ctg(5π/6) = 1/tg(5π/6
tg(5π/6) = tg(π - π/6) = -tg(π/6) = -√
Therefore, ctg(5π/6) = 1/(-√3) = -1/√3 = -√3/3
Find the value of tg(π/12)
tg(π/12) = sin(π/12) / cos(π/12)
We know the values of sin(π/12) and cos(π/12) are not easily simplified and therefore we will leave it as tg(π/12).
Find the value of ctg(π/12)
ctg(π/12) = 1/tg(π/12)
Find the value of tg(7π/4)
tg(7π/4) = tg(π + 3π/4) = tg(3π/4) = -1
Now putting all the values back into the original expression
√3 (-√3/3) + tg(π/12) 1/ tg(π/12) + 2 * (-1) +
= -3 + 1 + (-2) +
= -3 + 1 - 2 +
= -4
Therefore, the simplified value of the expression is -4.