Question

Cos6x-cos4x/ sin5x !!!

Answer 1

Ответ:

Ответ смотри во вложении

Answer 2

To simplify the expression $\frac{\cos(6x) - \cos(4x)}{\sin(5x)}$, you can use trigonometric identities and properties.

1. Start by using the trigonometric identity for the difference of cosines:

$\cos(A) - \cos(B) = -2\sin\left(\frac{A + B}{2}\right)\sin\left(\frac{A - B}{2}\right)$

In this case, let $A = 6x$ and $B = 4x$:

$\cos(6x) - \cos(4x) = -2\sin\left(\frac{6x + 4x}{2}\right)\sin\left(\frac{6x - 4x}{2}\right) = -2\sin(5x)\sin(x)$

So, the expression becomes:

$\frac{-2\sin(5x)\sin(x)}{\sin(5x)}$

2. Now, you can simplify further by canceling out the common factor of $\sin(5x)$ in the numerator and denominator:

$\frac{-2\cancel{\sin(5x)}\sin(x)}{\cancel{\sin(5x)}}$

The simplified expression is:

$-2\sin(x)$

So, $\frac{\cos(6x) - \cos(4x)}{\sin(5x)} = -2\sin(x)$.