Question

А)sin (α - β) = sin α · cos β - cos α · sin β Б) 1/2 sin α+cos•(pi/6+α) УПРОСТИТЬ ВЫРАЖЕНИЕ

Answer 1

1/2sina+cospi/6cosa-sinpi/6sina=1/2sina+V3/2cosa-1/2sina=V3/2cosa

а с 1) я так и не поняла, что делать?

Answer 2

A) sin (α + β) = sin α · cos β - cos α · sin β

The formula you provided is the addition formula for the sine function. It states that the sine of the sum of two angles (α + β) is equal to the product of the sine of the first angle (α) and the cosine of the second angle (β), minus the product of the cosine of the first angle (α) and the sine of the second angle (β).

This formula is derived from the trigonometric identities and can be proven using geometric reasoning or by using the Euler's formula for complex numbers.

Here is the formula again for reference: sin (α + β) = sin α · cos β - cos α · sin β

B) 1/2 sin α cos(pi/6 + α)

To simplify the expression 1/2 sin α cos(pi/6 + α), we can use the product-to-sum formula for trigonometric functions.

The product-to-sum formula states that: sin A · cos B = 1/2 [sin(A + B) + sin(A - B)]

Applying this formula to the given expression, we have: 1/2 sin α cos(pi/6 + α) = 1/2 [sin(α + pi/6 + α) + sin(α - pi/6 - α)]

Simplifying further, we get: 1/2 sin α cos(pi/6 + α) = 1/2 [sin(2α + pi/6) + sin(-pi/6)]

Since sin(-x) = -sin(x), we can simplify the expression to: 1/2 sin α cos(pi/6 + α) = 1/2 [sin(2α + pi/6) - sin(pi/6)]

And that is the simplified expression.

I hope this helps! Let me know if you have any further questions.