Question

Sin x/4П=0 cos (2П/3 -4х/30) = √2/2 sin (x/3 +П/18)= -1 tg (10 -5x)= -4 Ag (x+П/5)=1 4-4 sin9(x/6 - П/24)= 0

Answer 1

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Answer 2

It looks like you've provided a set of trigonometric equations. Let's solve each of them one by one:

1. $\frac{\sin(x)}{4\pi} = 0$ Since the numerator is 0, sin(x) must be 0. The solutions to this equation are $x = 0, \pi, 2\pi, \ldots$.

2. $\cos\left(\frac{2\pi}{3} - \frac{4x}{30}\right) = \frac{\sqrt{2}}{2}$ Using the cosine of a difference formula, this equation simplifies to $\cos\left(\frac{2\pi}{3}\right)\cos\left(\frac{4x}{30}\right) + \sin\left(\frac{2\pi}{3}\right)\sin\left(\frac{4x}{30}\right) = \frac{\sqrt{2}}{2}$. Simplifying further, you get $\frac{1}{2}\cos\left(\frac{4x}{30}\right) - \frac{\sqrt{3}}{2}\sin\left(\frac{4x}{30}\right) = \frac{\sqrt{2}}{2}$. To solve this equation, you can divide both sides by $\frac{\sqrt{2}}{2}$ to get $\cos\left(\frac{4x}{30}\right) - \sqrt{3}\sin\left(\frac{4x}{30}\right) = \sqrt{2}$. You can now use trigonometric identities to simplify this equation further and solve for $x$.

3. $\sin\left(\frac{x}{3} + \frac{\pi}{18}\right) = -1$ This equation implies $\frac{x}{3} + \frac{\pi}{18} = -\frac{\pi}{2} + 2\pi k$, where $k$ is an integer. Solve for $x$ in this case.

4. $\tan(10 - 5x) = -4$ Solve for $x$ using the arctangent function after rearranging the equation to isolate $x$.

5. $4 - 4\sin\left(\frac{9x}{6} - \frac{\pi}{24}\right) = 0$ Simplify and solve for $x$ using trigonometric identities.

Please note that solving trigonometric equations often involves applying various trigonometric identities and properties. If you need further assistance with any specific equation, please let me know!