Question

1)1cos17*cos13*-sin17*sin13*2)sin 38* cos 22*+cos38*sin22*(*-це градуси)​

Answer 1

1)Используем формулу косинуса суммы:

cos17°cos13°-sin17°sin13°= cos (17°+13°)= cos 30°= √3/2

2)Используем формулу синуса суммы:

sin 38°cos 22°+cos38°sin22°= sin (38°+22°)= sin 60°= √3/2

Answer 2

$1)$  $cos17^0cos13^0-sin17^0sin13^0=cos(17^0+13^0)=cos30^0=\frac{\sqrt{3} }{2}$

$2)$  $sin 38^0 cos 22^0+cos38^0sin22^0=sin(38^0+22^0)=sin60^0=\frac{\sqrt{3} }{2}$

Answer 3

It looks like you've provided two mathematical expressions involving trigonometric functions. Let's break down and simplify each expression:

1. $\cos(17^\circ) \cdot \cos(13^\circ) \cdot (-\sin(17^\circ)) \cdot (-\sin(13^\circ))$

First, let's simplify the negative signs: $\cos(17^\circ) \cdot \cos(13^\circ) \cdot \sin(17^\circ) \cdot \sin(13^\circ)$

This expression involves products of trigonometric functions. However, these specific angles might not result in any neat integer values. You would typically calculate this using a calculator or software capable of handling trigonometric functions and degrees.

2. $\sin(38^\circ) \cdot \cos(22^\circ) + \cos(38^\circ) \cdot \sin(22^\circ)$

This expression involves the sum of two products of trigonometric functions. You can use trigonometric identities to simplify it. One of the identities you can use is the sum formula for sine: $\sin(A + B) = \sin(A) \cdot \cos(B) + \cos(A) \cdot \sin(B)$

Comparing this identity with the given expression, we can see that it's almost the same. The only difference is the angles used. We can rewrite the expression using the identity: $\sin(38^\circ + 22^\circ)$

Calculate the sum of the angles: $38^\circ + 22^\circ = 60^\circ$

So, the simplified expression is: $\sin(60^\circ)$

And since $\sin(60^\circ) = \frac{\sqrt{3}}{2}$, the value of the second expression is $\frac{\sqrt{3}}{2}$.

Remember that trigonometric functions often involve angles in radians rather than degrees in more advanced mathematics. If you need a numerical approximation, you would typically use a calculator.