Question

70tg2a если tg a =6 решите уравнение

Answer 1

$70tg2a=70\cdot \frac{2tga}{1-tg^2a}=70\cdot \frac{12}{1-36}=-24$

Answer 2

To solve the equation 70tg^2(a) = 6 when tg(a) = 6, follow these steps:

Step 1: Substitute the value of tg(a) into the equation: 70 * (6)^2 = 70 * 36 = 2520

Step 2: Solve for 'a': tg^2(a) = 2520 / 70 = 36

Step 3: Take the square root of both sides to find tg(a): tg(a) = √36 = ±6

Since the tangent function is periodic, there are infinitely many solutions. The general solution for 'a' can be expressed as follows:

a = arctan(6) + kπ where 'k' is an integer.

For each integer value of 'k', you will get a different solution for 'a'. This is because the tangent function has a periodic behavior with a period of π (pi).

So, the equation 70tg^2(a) = 6 has multiple solutions for 'a', given by:

a = arctan(6) + kπ, where k is an integer.