Question

проверьте справедливость равенства синус 93 градусов минус синус 63 градусов равно синус 33 градусов​

Answer 1

Ответ:

Не справедливо

Объяснение:

Доказать: $sin(93^{\circ})-sin(63^{\circ})=sin(33^{\circ})$

Доказательство:

Воспользуемся формулой разности синусов:

$sin(\alpha)-sin(\beta)=2sin(\frac{\alpha-\beta}{2})cos(\frac{\alpha+\beta}{2})$

$sin(93^{\circ})-sin(63^{\circ})=2\cdot sin(\frac{93^{\circ}-63^{\circ}}{2})\cdot cos(\frac{93^{\circ}+63^{\circ}}{2})=2\cdot sin(15^{\circ})\cdot cos(78^{\circ})$

Не справедливо

Answer 2

#### Equality of Sinusoids To verify the equality **sin(93°) - sin(63°) = sin(33°)**, we can use the trigonometric identity: **sin(A) - sin(B) = 2 * cos((A + B)/2) * sin((A - B)/2)** Let's substitute the given angles into the formula: **sin(93°) - sin(63°) = 2 * cos((93° + 63°)/2) * sin((93° - 63°)/2)** Simplifying the equation: **sin(93°) - sin(63°) = 2 * cos(78°) * sin(15°)** Now, let's calculate the values of **cos(78°)** and **sin(15°)**: Using a scientific calculator or trigonometric tables, we find that: **cos(78°) ≈ 0.2079**. **sin(15°) ≈ 0.2588**. Substituting these values back into the equation: **sin(93°) - sin(63°) ≈ 2 * 0.2079 * 0.2588** **sin(93°) - sin(63°) ≈ 0.1074** The approximate value of **sin(93°) - sin(63°)** is **0.1074**. Now, let's calculate the value of **sin(33°)**: Using a scientific calculator or trigonometric tables, we find that: **sin(33°) ≈ 0.5446**. Comparing the calculated value of **sin(93°) - sin(63°)** with **sin(33°)**: **0.1074 ≈ 0.5446** The calculated value of **sin(93°) - sin(63°)** is not equal to **sin(33°)**. Therefore, the statement **sin(93°) - sin(63°) = sin(33°)** is not true. Please note that the values used in this calculation are approximate, and the actual values may have more decimal places.