Question

(Sin〖285〗^0*cos〖375〗^0- cos〖105〗^0* Sin〖165〗^0+ cos〖330〗^0)2 +4

Answer 1

Ответ на картинке внизу страницы

Answer 2

Let's simplify the given expression step by step:

1. Convert the angles from degrees to radians: sin(285°) = sin(285° * π/180) ≈ sin(4.97419) cos(375°) = cos(375° * π/180) ≈ cos(6.54499) cos(105°) = cos(105° * π/180) ≈ cos(1.8326) sin(165°) = sin(165° * π/180) ≈ sin(2.87979) cos(330°) = cos(330° * π/180) ≈ cos(5.75959)

2. Evaluate the trigonometric functions: sin(4.97419) ≈ -0.917214 cos(6.54499) ≈ 0.809017 cos(1.8326) ≈ 0.364309 sin(2.87979) ≈ 0.24869 cos(5.75959) ≈ 0.707107

3. Substitute the values back into the expression: (-0.917214 * 0.809017 - 0.364309 * 0.24869 + 0.707107)^2 + 4

4. Perform the arithmetic operations: (-0.741771 - 0.090537 + 0.707107)^2 + 4 (-0.125201)^2 + 4 0.015662 + 4 4.015662

So, the simplified expression is approximately 4.015662.