Question

3cos215-4cos35-2sin125/cos17×cos18-cos73×cos72

Answer 1

Решение во вложении------------------

Answer 2

To simplify the given expression:

1. Let's start by simplifying the numerator: 3cos(215) - 4cos(35) - 2sin(125)

   Remember that cosine is an even function, which means cos(-x) = cos(x). So we can rewrite the expression as:

   3cos(215) - 4cos(35) - 2sin(125) 3cos(-145) - 4cos(35) - 2sin(125) 3cos(145) - 4cos(35) - 2sin(125)

2. Now let's simplify the denominator: cos(17) × cos(18) - cos(73) × cos(72)

   Again, using the property of even functions, we can rewrite the expression as:

   cos(17) × cos(18) - cos(73) × cos(72) cos(-17) × cos(18) - cos(-73) × cos(72) cos(17) × cos(18) - cos(73) × cos(72)

3. Finally, we can simplify the expression by substituting the values of the trigonometric functions:

   Numerator: 3cos(145) - 4cos(35) - 2sin(125)

   Denominator: cos(17) × cos(18) - cos(73) × cos(72)

   Evaluating the trigonometric functions, we get:

   Numerator: 3(-0.819) - 4(0.819) - 2(-0.819) -2.457 - 3.276 + 1.638 -4.095

   Denominator: cos(17) × cos(18) - cos(73) × cos(72) 0.961 × 0.951 - (-0.406) × 0.309 0.914 - (-0.125) 0.914 + 0.125 1.039

4. Putting it all together, the simplified expression is:

   (-4.095) / (1.039) ≈ -3.945