Question

Sin^2 pi/4 cos(-pi/3)+2cos pi/6

Answer 1

Решение
Sin^2 pi/4 cos(-pi/3)+2cos pi/6 = (1 / √2)² * (1/2) + 2 * (√3/2) = 1/4 + √3

Answer 2

Let's simplify the expression step by step:

1. First, let's recall some trigonometric identities:

   • sin(pi/4) = cos(pi/4) = 1/sqrt(2)
   • cos(-pi/3) = cos(pi/3) = 1/2
   • cos(pi/6) = sqrt(3)/2

2. Now, we can substitute these values into the expression:

   sin^2(pi/4) * cos(-pi/3) + 2 * cos(pi/6)

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

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

   = 1/4 + sqrt(3)

So, the simplified value of the expression is 1/4 + sqrt(3).