Question

Cos 19π\12-sin 5π\12​

Answer 1

Ответ:

$- \frac{ \sqrt{2} }{2}$

Answer 2

To find the value of cos(19π/12) - sin(5π/12), you can use trigonometric identities and simplification.

1. First, let's find the values of cos(19π/12) and sin(5π/12):

cos(19π/12) can be expressed as follows: cos(19π/12) = cos(π - π/12) = -cos(π/12)

sin(5π/12) can be expressed as follows: sin(5π/12) = sin(π - π/12) = sin(π/12)

2. Now, you can use the trigonometric identity: sin(π/2 - θ) = cos(θ) for any angle θ.

So, cos(π/12) is equal to sin(π/2 - π/12), which means:

cos(π/12) = sin(π/2 - π/12) = sin(π/3) = √3/2.

3. Similarly, you can find sin(π/12) as:

sin(π/12) = sin(π/2 - π/12) = sin(π/3) = √3/2.

4. Now, you can calculate the value of cos(19π/12) and sin(5π/12):

cos(19π/12) = -cos(π/12) = -(-√3/2) = √3/2.

sin(5π/12) = sin(π/12) = √3/2.

5. Finally, calculate the expression:

cos(19π/12) - sin(5π/12) = (√3/2) - (√3/2) = 0.

So, cos(19π/12) - sin(5π/12) is equal to 0.