Sin(P/6 + x) - sin(P/6 -x)=1

Предыдущий
вопрос Следующий
вопрос

To find a solution to the equation sin(P/6 + x) - sin(P/6 -x) = 1, we can use the sum-to-product identities for sine:

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

Applying this identity to the given equation, we get:

2cos(P/6)sin(x) = 1

Dividing both sides by 2cos(P/6), we get:

sin(x) = 1 / (2cos(P/6))

Now, we know that cos(P/6) = sqrt(3)/2 (since P = pi), so plugging this into the equation we get:

sin(x) = 1 / (2 * sqrt(3) / 2
sin(x) = 1 / sqrt(3
sin(x) = sqrt(3) / 3

Therefore, the solution to the equation sin(P/6 + x) - sin(P/6 - x) = 1 is sin(x) = sqrt(3) / 3.