Question

3. [4 6anna] Bbychute: a) COS40°cos20° - sin40°sin 20° 6) sin 105°​

Answer 1

Ответ:

решение смотри на фотографии

Answer 2

It seems like you have a mathematical expression and a trigonometric question. Let's break it down step by step.

1. COS40°cos20° - sin40°sin20°:

   To simplify this expression, you can use the trigonometric identity for the cosine of the difference of two angles:

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

   In your case, A = 40° and B = 20°, so:

   cos(40° - 20°) = cos(20°)cos(40°) + sin(20°)sin(40°)

   Now, you can calculate the values of cos(20°) and sin(40°) using a calculator or reference tables. Once you have those values, you can perform the calculation.

2. sin 105°:

   To find the value of sin(105°), you can use the sum-to-product trigonometric identity:

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

   In your case, A = 60° and B = 45° (105° = 60° + 45°), so:

   sin(105°) = sin(60°)cos(45°) + cos(60°)sin(45°)

   Calculate the values of sin(60°), cos(45°), and sin(45°) using a calculator or reference tables, and then perform the calculation.

Please note that trigonometric values are typically expressed in decimals or fractions, so you may need to convert between degrees and radians if necessary. If you have specific numerical values for the angles, you can substitute them into the equations to find the exact results.