Question

Sin pi/6 * cos pi/12 + cos pi/6 * sin pi/12

Answer 1

Ответ:

$\sqrt{2} /2$

Объяснение:

sin(p/6)*cos(p/12)+cos(p/6)*sin(p/12)=sin(p/6+p/12)=sin(p/4)=$\sqrt{2} /2$

Answer 2

To evaluate the expression sin(pi/6) * cos(pi/12) + cos(pi/6) * sin(pi/12), we can use the trigonometric identities for the sum of angles.

Let's break down the expression step by step:

sin(pi/6) * cos(pi/12) + cos(pi/6) * sin(pi/12)

We know that sin(a + b) = sin(a) * cos(b) + cos(a) * sin(b). Comparing this with our expression, we can see that a = pi/6 and b = pi/12.

sin(pi/6) * cos(pi/12) + cos(pi/6) * sin(pi/12) = sin(pi/6 + pi/12)

We can simplify pi/6 + pi/12:

pi/6 + pi/12 = 2pi/12 + pi/12 = 3pi/12 = pi/4

Therefore, the expression simplifies to:

sin(pi/6) * cos(pi/12) + cos(pi/6) * sin(pi/12) = sin(pi/4)

The sine of pi/4 is equal to 1/sqrt(2) or approximately 0.7071.

So, the final value of the expression is approximately 0.7071.