Question

6) cos 46°- cos 74°=​

Answer 1

Ответ:

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\/3        *sin(14*)=0.419021

Объяснение:

Answer 2

To calculate the value of $\cos 46° - \cos 74°$, you can use trigonometric identities and properties. The identity that will be useful here is:

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

In this case, $A = 60°$ and $B = 74°$, so:

$\cos 46° - \cos 74° = -2 \cdot \sin\left(\frac{46°+74°}{2}\right) \cdot \sin\left(\frac{46°-74°}{2}\right)$

$= -2 \cdot \sin 60° \cdot \sin (-14°)$

Since $\sin 60° = \frac{\sqrt{3}}{2}$ and $\sin (-14°) = -\sin 14°$, the expression becomes:

$= -2 \cdot \frac{\sqrt{3}}{2} \cdot (-\sin 14°)$

$= \sqrt{3} \cdot \sin 14°$

Now you can use a calculator to approximate the value of $\sin 14°$ and then multiply it by $\sqrt{3}$ to get the final result. Keep in mind that trigonometric functions are typically given in decimal form.

Using a calculator, you would find that $\sin 14° \approx 0.2419$, so:

$\sqrt{3} \cdot \sin 14° \approx 0.2419 \cdot \sqrt{3} \approx 0.4184$

Therefore, $\cos 46° - \cos 74° \approx 0.4184$.