Question

(sin 195°- sin 165°)×sin 15°

Answer 1

Объяснение:

$(sin195^0-sin165^0)*sin15^0=2*sin\frac{195^0-165^0}{2} *cos\frac{195^0+165^0}{2} =sin15^0=\\=2*sin15^0*cos360^0*sin15^0=2*sin^215^0.$

Answer 2

To calculate the expression $(\sin 195° - \sin 165°) \times \sin 15°$, you can follow these steps:

1. Use the trigonometric identity $\sin(A - B) = \sin A \cos B - \cos A \sin B$.
2. Apply this identity to the expression $\sin 195° - \sin 165°$.

Let's go through the calculations:

$$\begin{align*} \sin(195° - 165°) &= \sin 195° \cos 165° - \cos 195° \sin 165° \\ &= (\sin 195° \cos 165°) - (\cos 195° \sin 165°). \end{align*}$$

3. Now, multiply the result by $\sin 15°$:

$$\text{Final result} = (\sin 195° \cos 165° - \cos 195° \sin 165°) \times \sin 15°.$$

Unfortunately, these calculations involve specific trigonometric values, and the result cannot be simplified further without numerical values for $\sin 195°$, $\cos 165°$, $\cos 195°$, and $\sin 165°$. You can use a calculator to find the numerical result for this expression.