Question

Sin 105 градусов - sin 15 градусов

Answer 1

Там посреднике формула. Формула преобразования алгебраической суммы тригонометрических функций в произведение

Answer 2

To find the value of sin 105 degrees - sin 15 degrees, we can use the trigonometric identity:

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

In this case, A = 105 degrees and B = 15 degrees.

sin 105 degrees - sin 15 degrees = sin (105 degrees - 15 degrees)

Now, let's find the sine and cosine of 105 degrees and 15 degrees:

sin 105 degrees = 0.96592582628 cos 105 degrees = 0.2588190451

sin 15 degrees = 0.2588190451 cos 15 degrees = 0.96592582628

Now, substitute these values into the identity:

sin (105 degrees - 15 degrees) = sin 90 degrees

Since the sine of 90 degrees is 1:

sin 105 degrees - sin 15 degrees = 1 - 0.2588190451 = 0.7411809549

So, sin 105 degrees - sin 15 degrees is approximately 0.7412.