Question

Sin 15*cos 15 (градусов)

Answer 1

Sin15*cos15=1/2(sin(15-15)+sin(15+15))=1/2(sin0+sin30)=2=1/2(0+1/2)=1/2*1/2=1/4

Answer 2

To calculate the value of sin(15°) * cos(15°), we can use the trigonometric identity:

sin(2θ) = 2 * sin(θ) * cos(θ)

Let's apply this identity to our expression:

sin(15°) * cos(15°) = (1/2) * 2 * sin(15°) * cos(15°)

Now, let's rewrite sin(15°) and cos(15°) in terms of sin(30°) and cos(30°) using another trigonometric identity:

sin(30°) = 1/2 cos(30°) = √3/2

sin(15°) = sin(30°/2) = √((1 - cos(30°))/2) cos(15°) = cos(30°/2) = √((1 + cos(30°))/2)

Substituting these values back into our expression:

sin(15°) * cos(15°) = (1/2) * 2 * √((1 - cos(30°))/2) * √((1 + cos(30°))/2)

Simplifying further:

sin(15°) * cos(15°) = √((1 - cos(30°)) * (1 + cos(30°))) / 2

Now, let's substitute the values of cos(30°):

sin(15°) * cos(15°) = √((1 - √3/2) * (1 + √3/2)) / 2

sin(15°) * cos(15°) = √((2 - √3) * (2 + √3)) / 2

sin(15°) * cos(15°) = √(4 - 3) / 2

sin(15°) * cos(15°) = √1 / 2

Finally, we can simplify it further:

sin(15°) * cos(15°) = 1/2

Therefore, sin(15°) * cos(15°) is equal to 1/2.