Question

Решите: 8sin15°sin75°

Answer 1

8sin15°sin75°=4*(cos(15°-75°)-cos(15°+75°))=4*(cos(-60°)-cos90°)=4(cos60°-0)=4*1/2=2

Answer 2

To solve the expression 8sin15°sin75°, we can use the trigonometric identity for the product of two sines:

sin(A)sin(B) = (1/2)[cos(A-B) - cos(A+B)]

Let's substitute the values A = 15° and B = 75° into the identity:

sin(15°)sin(75°) = (1/2)[cos(15°-75°) - cos(15°+75°)]

Simplifying further:

sin(15°)sin(75°) = (1/2)[cos(-60°) - cos(90°)]

Now, we know that cos(-θ) = cos(θ), so we can rewrite the expression as:

sin(15°)sin(75°) = (1/2)[cos(60°) - cos(90°)]

The value of cos(60°) is 1/2, and cos(90°) is 0, so we have:

sin(15°)sin(75°) = (1/2)(1/2 - 0) = (1/2)(1/2) = 1/4

Therefore, the value of 8sin15°sin75° is 8 * (1/4) = 2.