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Exercise

$\frac{\sin\left(x+y\:\right)-\sin\left(x\right)}{y}$

Step-by-step Solution

1

Apply the trigonometric identity: $\sin\left(a\right)-\sin\left(b\right)$$=2\sin\left(\frac{a-b}{2}\right)\cos\left(\frac{a+b}{2}\right)$, where $a=x+y$ and $b=x$

$\frac{2\sin\left(\frac{x+y-x}{2}\right)\cos\left(\frac{x+y+x}{2}\right)}{y}$
2

Cancel like terms $x$ and $-x$

$\frac{2\sin\left(\frac{y}{2}\right)\cos\left(\frac{x+y+x}{2}\right)}{y}$
3

Combining like terms $x$ and $x$

$\frac{2\sin\left(\frac{y}{2}\right)\cos\left(\frac{2x+y}{2}\right)}{y}$

Final answer to the exercise

$\frac{2\sin\left(\frac{y}{2}\right)\cos\left(\frac{2x+y}{2}\right)}{y}$

Try other ways to solve this exercise

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  • Find the roots
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