Question

Sin(п/3+a)- корень 3/2 cos a

Answer 1

Используй формулу синуса суммы 2 углов
=sin(П/3)cosa+cos(П/3)sina-(кор из 3)/2cosa=
=(кор из 3)/2 *cosa+(1/2) *sina-(кор из 3)/2 *cosa=(1/2) *sina.

Answer 2

To verify the given equation:

sin(π/3 + a) = √3/2 cos(a)

We can use the trigonometric identity:

sin(α + β) = sin(α)cos(β) + cos(α)sin(β)

Using this identity, we can rewrite the left side of the equation as:

sin(π/3 + a) = sin(π/3)cos(a) + cos(π/3)sin(a)

We know that sin(π/3) = √3/2 and cos(π/3) = 1/2. Substituting these values, we get:

sin(π/3 + a) = (√3/2)cos(a) + (1/2)sin(a)

Now let's compare this expression with the right side of the equation:

√3/2 cos(a) = (√3/2)cos(a)

We can see that the expressions on both sides of the equation are the same, so the given equation holds true:

sin(π/3 + a) = √3/2 cos(a)