Question

Cos(x-180)= tg(x-270)= ctg(2п+x)=

Answer 1

Cos(x-180)= - cosx
tg(x-270)= - ctgx
ctg(2П+x)= ctgx

Answer 2

To solve this problem, we need to use some trigonometric identities and simplify each expression:

1. Cos(x-180) = -cos(x) Using the identity cos(x - 180) = -cos(x), we can rewrite the first expression as -cos(x).

2. tg(x-270) = -cot(x) Using the identity tg(x - 270) = -cot(x), we can rewrite the second expression as -cot(x).

3. ctg(2п+x) = -tan(x) Using the identity ctg(2π + x) = -tan(x), we can rewrite the third expression as -tan(x).

Therefore, the three expressions can be simplified as follows:

• Cos(x-180) = -cos(x)
• tg(x-270) = -cot(x)
• ctg(2п+x) = -tan(x)

Note that all three expressions have a negative sign in front of them, which means that they are equivalent to the opposite of the corresponding trigonometric function. So, we can rewrite the expressions without the negative sign:

• Cos(x-180) = cos(x)
• tg(x-270) = cot(x)
• ctg(2п+x) = tan(x)

Therefore, the solutions for x are any angle for which the above equations hold. For example, if we take x = 0, then we have:

• Cos(0-180) = cos(0) -> -1 = 1 (false)
• tg(0-270) = cot(0) -> undefined = 1/0 (false)
• ctg(2π+0) = tan(0) -> -∞ = 0 (false)

So, there is no real solution for x that satisfies all three equations simultaneously.