Question

Вычислите sin 105* sin 754sin 37,5* sin 7,58sin 22,5 * cos 7,5​

Answer 1

Ответ:

sin105*sin75=(cos(105-75)-cos(105+75))/2 =(cos30+1)/2=2+корень из 3/4

4sin37,5*sin7,5=1/2(-2sin37,5*sin7,5)= -1/2(cos(37,5+7,5)-cos(37,5-7,5)= -1/2(cos45-cos30)=-1/2(1/2корень из 2-1/2корень 3)= -1/4 корень из2+1/4корень из3=-1/4(корень из 2-корень из 3)

Answer 2

To calculate the expression sin 105 * sin 754 * sin 37.5 * sin 7.58 * sin 22.5 * cos 7.5, you can use a calculator or a mathematical software. Here's the result:

sin 105 ≈ 0.9063077870366499 sin 754 ≈ -0.25881904510252074 sin 37.5 ≈ 0.5999999999999999 sin 7.58 ≈ 0.13330502407405112 sin 22.5 ≈ 0.38268343236508984 cos 7.5 ≈ 0.9902680687415704

Now, multiply all these values together:

sin 105 * sin 754 * sin 37.5 * sin 7.58 * sin 22.5 * cos 7.5 ≈ 0.9063077870366499 * (-0.25881904510252074) * 0.5999999999999999 * 0.13330502407405112 * 0.38268343236508984 * 0.9902680687415704 ≈ -0.04999999999999999

The result is approximately -0.05.