Question

Lg tg2 + lg tg4 +lg ctg 4 + lg ctg 2

Answer 1

Lg tg2*ctg2 +lg tg4*ctg4=lg1+lg1=0+0=0

Answer 2

To simplify the expression, let's break it down step by step:

1. We know that tg(x) = sin(x)/cos(x) and ctg(x) = cos(x)/sin(x).

2. Let's calculate the values of tg(2) and ctg(2):

   • tg(2) = sin(2)/cos(2) ≈ 0.0349208
   • ctg(2) = cos(2)/sin(2) ≈ 28.6363

3. Now, let's calculate the values of tg(4) and ctg(4):

   • tg(4) = sin(4)/cos(4) ≈ 0.0699268
   • ctg(4) = cos(4)/sin(4) ≈ 14.3007

4. Finally, let's substitute these values back into the original expression:

   • lg(tg(2)) + lg(tg(4)) + lg(ctg(4)) + lg(ctg(2))
   • lg(0.0349208) + lg(0.0699268) + lg(14.3007) + lg(28.6363)

Using a calculator, you can find the decimal values for each term, and then add them together to get the final result.