Question

Cos15°sin20°-sin15°cos20° ______________________ 2sin355 надо вычислить

Answer 1

$\displaystyle \frac{\cos15а\sin20а-\sin15а\cos20а}{2\sin355а}=\frac{\sin(20а-15а)}{2\sin(360а-5а)}=\frac{\sin5а}{-2\sin5а}=-0.5$

Answer 2

Let's simplify the expression step by step:

1. We can start by using the trigonometric identities for the sine and cosine of the sum of angles:

sin(A + B) = sin(A)cos(B) + cos(A)sin(B) cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

2. Apply these identities to the expression:

Cos(15°)sin(20°) - sin(15°)cos(20°) = sin(15° + 20°) = sin(35°)

3. Now, let's simplify the denominator:

2sin(355°) = 2sin(360° - 5°)

Since the sine function is periodic with a period of 360°:

sin(360° - 5°) = sin(-5°)

But sine is an odd function, meaning sin(-x) = -sin(x):

sin(-5°) = -sin(5°)

Now, the expression becomes:

2sin(355°) = 2 * (-sin(5°)) = -2sin(5°)

So, the final expression is:

sin(35°) / (-2sin(5°))

Note: The angle 355° may seem unusual in conventional trigonometry, as angles are typically measured within a range of 0° to 360°. However, mathematically, it is valid to express angles in this way, where 355° is equivalent to -5° due to the periodic nature of trigonometric functions.