# How do you simplify #(sin6x)/(sin5x) #?

sinx.cot 5x + cos x

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To simplify ( \frac{\sin(6x)}{\sin(5x)} ), you can use the trigonometric identity:

[ \frac{\sin(a)}{\sin(b)} = \frac{\sin(a)}{\sin(b)} \times \frac{b}{b} = \frac{\sin(a)}{\sin(b)} \times \frac{1}{\frac{b}{a}} ]

Applying this identity to the given expression:

[ \frac{\sin(6x)}{\sin(5x)} = \frac{\sin(6x)}{\sin(5x)} \times \frac{1}{\frac{5x}{6x}} ]

[ = \frac{\sin(6x)}{\sin(5x)} \times \frac{1}{\frac{5}{6}} ]

[ = \frac{\sin(6x)}{\sin(5x)} \times \frac{6}{5} ]

So, ( \frac{\sin(6x)}{\sin(5x)} ) simplifies to ( \frac{6}{5} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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