Question

1) sin170°+sin10°2)sin230°-sin50°3)cos25°-cos65°​

Answer 1

180
180
-40
Так на калькуляторі

Answer 2

Let's calculate the values of the expressions you've provided:

1. sin(170°) + sin(10°):

sin(170°) is equal to sin(180° - 10°). Since sin is an odd function, sin(180° - θ) = -sin(θ), so sin(170°) = -sin(10°). Therefore,

sin(170°) + sin(10°) = -sin(10°) + sin(10°) = 0

2. sin(230°) - sin(50°):

sin(230°) is equal to sin(180° + 50°). Since sin is an odd function, sin(180° + θ) = sin(θ), so sin(230°) = sin(50°). Therefore,

sin(230°) - sin(50°) = sin(50°) - sin(50°) = 0

3. cos(25°) - cos(65°):

cos(25°) - cos(65°) cannot be simplified to 0 directly because the cosines have different arguments. To calculate the difference, you can use the trigonometric identity:

cos(A) - cos(B) = -2 * sin((A + B) / 2) * sin((A - B) / 2)

In this case, A = 25° and B = 65°:

cos(25°) - cos(65°) = -2 * sin((25° + 65°) / 2) * sin((25° - 65°) / 2)

First, calculate the values inside the sine functions:

sin((25° + 65°) / 2) = sin(90° / 2) = sin(45°) = √2/2

sin((25° - 65°) / 2) = sin(-20° / 2) = sin(-10°) = -sin(10°)

Now, plug these values into the expression:

-2 * (√2/2) * (-sin(10°)) = √2 * sin(10°)

So, the value of cos(25°) - cos(65°) is √2 * sin(10°).