Question

sin (x+pi/12)=0 general solution

Answer 1

$Good \: \: \: \: Afternoon \: \: \\ \\ \sin(x + \pi \div 12) = 0 \\ \\ \sin(x + \pi \div 12) = \sin(0) \div becoz \: \: \sin(0) = 0 \\ \\ (x + \pi \div 12) = n\pi + ( - 1) {}^{n} \times 0 \\ \\ (x + \pi \div 12) = n\pi \\ \\ x = n\pi - (\pi \div 12) \\ \\ x = (12n\pi - \pi) \div 12 \\ \\ \\ if \: \: \: \: \: \sin( \alpha ) = \sin( \beta ) \\ \\ \alpha = n\pi + ( - 1) {}^{n} \beta$

Answer 2

The solution of the equation is $x=\frac{12n\pi-\pi}{12}$.

Step-by-step explanation:

Given : Equation $\sin(x+\frac{\pi}{12})=0$

To find : The general solution of the equation ?

Solution :

The general solution of $\sin x=0$ is $x=n\pi$ where n∈I.

So, the solution of the equation $\sin(x+\frac{\pi}{12})=0$ is

$x+\frac{\pi}{12}=n\pi$

$x=n\pi-\frac{\pi}{12}$

$x=\frac{12n\pi-\pi}{12}$

Therefore, the solution of the equation is $x=\frac{12n\pi-\pi}{12}$.

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