Question

Найти tg2a , если ctga=-2

Answer 1

Ответ:

Пошаговое объяснение:

tg(2a)= 2tg(a)/(1-tg²(a))

ctg(a)= 1/tg(a)

-2= 1/tg(a)

tg(a)= -0,5

tg(2a)= 2*(-0,5)/(1-(-0,5)²)= -1/0,75= - 1 1/3

Answer 2

Ответ:

-4/3

Пошаговое объяснение:

$ctga=-2=>tga=\frac{1}{ctga}=\frac{1}{-2}=-\frac{1}{2}\\\\tg2a=\frac{2tga}{1-tg^2a}\\\\tg2a=\frac{2*(-1/2)}{1-(-1/2)^2}=\frac{-1}{1-(1/4)}=\frac{-1}{3/4}=-\frac{4}{3}$

Answer 3

To find the value of tg(2a) (which represents the tangent of twice the angle a), given that ctg(a) = -2, we can use trigonometric identities to express tg(2a) in terms of ctg(a).

The identity we'll use is:

tg(2a) = 2 * ctg(2a) / (1 - ctg^2(2a))

Now, we need to find ctg(2a). The cotangent of an angle is the reciprocal of its tangent. So, if ctg(a) = -2, then tg(a) = -1/2.

We can now calculate tg(2a):

Step 1: Find tg(a): tg(a) = -1/2

Step 2: Use the double angle formula for tangent: tg(2a) = 2 * tg(a) / (1 - tg^2(a))

Step 3: Substitute the value of tg(a): tg(2a) = 2 * (-1/2) / (1 - (-1/2)^2)

Step 4: Simplify: tg(2a) = -1 / (1 - 1/4) tg(2a) = -1 / (3/4)

Step 5: Invert the denominator and multiply: tg(2a) = -4/3

So, the value of tg(2a) is -4/3.