Question

3ctgx=0 2tgx-2ctgx=3

Answer 1

...................................

Answer 2

To solve the system of equations:

1. 3ctgx = 0
2. 2tgx - 2ctgx = 3

Let's work through the solution step by step.

Starting with equation 1:

3ctgx = 0

Since the product of two numbers is zero if and only if at least one of the numbers is zero, we can have two cases:

Case 1: c ≠ 0 In this case, we can divide both sides of equation 1 by 3c to isolate tg(x): tgx = 0/(3c) = 0

Case 2: c = 0 If c is zero, then equation 1 becomes 0 = 0. In this case, we have no information about the value of tg(x).

Now, let's move on to equation 2:

2tgx - 2ctgx = 3

We can factor out 2tgx from the left side:

2tgx(1 - ctgx) = 3

Divide both sides by (1 - ctgx):

2tgx = 3/(1 - ctgx)

Now, let's substitute the value of tg(x) from case 1:

2(0) = 3/(1 - c(0))

0 = 3/(1 - 0)

0 = 3/1

This equation is not satisfied, so the value of c must be 0.

In conclusion, if 3ctgx = 0 and 2tgx - 2ctgx = 3, then c must be equal to 0. However, we cannot determine the value of tg(x) based on the given equations.