Question

Cos(30° + a) - cos(30-a)​

Answer 1

Ответ:

$cos(30^\circ +a)-cos(30^\circ -a)=\\\\=(\underline {cos30^\circ \cdot cosa}-sin30^\circ \cdot sina)-(\underline{cos30^\circ \cdot cosa}+sin30^\circ \cdot sina)=\\\\=-2\cdot sin30^\circ \cdot sina=-2\cdot \dfrac{1}{2}\cdot sina=-sina$

Answer 2

Ответ:

cos(30°+a)-cos(30°-a) = (cos × 30° × cos × a - sin × 30° × sin × a) - ( cos × 30° × cos × a + sin × 30° × sin × a) = -2 × sin × 30° × sin × a = -2 × 1/2 × sin × a = - sin × a.

Answer 3

To simplify the expression $\cos(30^\circ + a) - \cos(30^\circ - a)$, you can use the sum and difference identities for cosine. The sum identity is:

$\cos(A + B) = \cos(A)\cos(B) - \sin(A)\sin(B)$

And the difference identity is:

$\cos(A - B) = \cos(A)\cos(B) + \sin(A)\sin(B)$

In your expression, $A = 30^\circ$ and $B = a$, so we can apply these identities:

$\cos(30^\circ + a) - \cos(30^\circ - a) = [\cos(30^\circ)\cos(a) - \sin(30^\circ)\sin(a)] - [\cos(30^\circ)\cos(a) + \sin(30^\circ)\sin(a)]$

Now, let's calculate each part separately:

1. $\cos(30^\circ)\cos(a) - \sin(30^\circ)\sin(a)$:

   $\cos(30^\circ) = \frac{\sqrt{3}}{2}$ $\sin(30^\circ) = \frac{1}{2}$

   So,

   $\cos(30^\circ)\cos(a) - \sin(30^\circ)\sin(a) = \frac{\sqrt{3}}{2} \cos(a) - \frac{1}{2} \sin(a)$

2. $\cos(30^\circ)\cos(a) + \sin(30^\circ)\sin(a)$:

   $\cos(30^\circ)\cos(a) + \sin(30^\circ)\sin(a) = \frac{\sqrt{3}}{2} \cos(a) + \frac{1}{2} \sin(a)$

Now, subtract the second expression from the first:

$\frac{\sqrt{3}}{2} \cos(a) - \frac{1}{2} \sin(a) - \left(\frac{\sqrt{3}}{2} \cos(a) + \frac{1}{2} \sin(a)\right)$

This simplifies to:

$\frac{\sqrt{3}}{2} \cos(a) - \frac{1}{2} \sin(a) - \frac{\sqrt{3}}{2} \cos(a) - \frac{1}{2} \sin(a)$

Now, combine like terms:

$\frac{\sqrt{3}}{2} \cos(a) - \frac{\sqrt{3}}{2} \cos(a) - \frac{1}{2} \sin(a) - \frac{1}{2} \sin(a)$