Question

Tg^2 п/4+2sin п/12*cos п/12-ctg^2 п/4

Answer 1

Tg^2 п/4+2sin п/12*cos п/12-ctg^2 п/4 =

=1 + Sin π/6 -1 = 1/2

Answer 2

To simplify the expression, let's use some trigonometric identities:

1. tg^2(π/4) = 1
2. sin(π/12) = (sqrt(3) - 1) / (2 * sqrt(2))
3. cos(π/12) = (sqrt(3) + 1) / (2 * sqrt(2))
4. ctg^2(π/4) = 1

Now, we can plug in these values into the given expression:

Tg^2(π/4) + 2sin(π/12) * cos(π/12) - ctg^2(π/4)

= 1 + 2 * ( (sqrt(3) - 1) / (2 * sqrt(2)) ) * ( (sqrt(3) + 1) / (2 * sqrt(2)) ) - 1

= 1 + (sqrt(3) - 1)(sqrt(3) + 1) / (2 * 2 * 2)

= 1 + (3 - 1) / 4

= 1 + 2/4

= 1 + 1/2

= 1.5

So, the simplified value of the expression is 1.5.