Question

Чему равен tg(3 альфа) если ctg альфа равен 3?очень срочно

Answer 1

Если ctg α=3, то tg α=1/3
tg2α=2tgα/(1-tg²α)=2/3 : (1-  1/9)=2/3 : 8/9=3/4

tg3α=tg(2α+α)=(tg2α+tgα)/(1-tgα·tg2α)=(3/4+1/3): (1-1/3·3/4)=13/12 : (1- 1/4)=13/9

Answer 2

Calculating tg(3*alpha) when ctg(alpha) = 3

To calculate the value of tg(3*alpha) when ctg(alpha) is equal to 3, we can use the relationship between tangent (tg) and cotangent (ctg) functions. The relationship between these two functions is as follows:

ctg(alpha) = 1 / tg(alpha)

Given that ctg(alpha) = 3, we can find tg(alpha) by taking the reciprocal of 3:

tg(alpha) = 1 / ctg(alpha) = 1 / 3

Now, to find tg(3*alpha), we can use the trigonometric identity:

tg(3*alpha) = tg(alpha + alpha + alpha)

Using the addition formula for tangent:

tg(3*alpha) = (tg(alpha) + tg(alpha) + tg(alpha) - tg(alpha) * tg(alpha) * tg(alpha)) / (1 - tg(alpha) * tg(alpha) - tg(alpha) * tg(alpha) - tg(alpha) * tg(alpha))

Substituting the value of tg(alpha) = 1/3 into the formula, we can calculate tg(3*alpha).

Calculation

Using the value of tg(alpha) = 1/3, we can calculate tg(3*alpha) using the formula mentioned above.