Question

1)SinП/4cosП/4ctgП/3;

Answer 1

sin(π/4)=cos(π/4)=(√2)/2 , ctg(π/3)=(√3)/3

(√2)/2 × (√2)/2 × (√3)/3=(√2)(√2)(√3)/(2×2×3)=(2√3)/12=(√3)/6

Answer 2

To evaluate the expression, let's first clarify the notation. I assume "П" is meant to represent the Greek letter "π" (pi) and "ctg" refers to the cotangent function.

The expression is:

1. sin(π/4) * cos(π/4) * cot(π/3)

Now, let's calculate each trigonometric value:

1. sin(π/4) = √2/2
2. cos(π/4) = √2/2

For cot(π/3), we need to recall the relationship between cotangent and tangent:

cot(θ) = 1 / tan(θ)

3. tan(π/3) = √3

Now, cot(π/3):

cot(π/3) = 1 / √3

Now, let's put it all together:

1. sin(π/4) * cos(π/4) * cot(π/3) = (√2/2) * (√2/2) * (1/√3) = (2/4) * (1/√3) = 1/2√3 = √3/6

So, the simplified value of the expression is √3/6.