Question

TAN 6X VALUE IF X IS PIE/ 48

Answer 1

sqrt(2) - 1

Answer 2

Given $x = \frac{\pi}{48}$, we need to find $\tan(6x)$. Calculate the angle: $6x = 6 \times \frac{\pi}{48} = \frac{\pi}{8}$. Use the half-angle identity: $\tan(\frac{\theta}{2}) = \frac{1 - \cos\theta}{\sin\theta}$. Let $\frac{\theta}{2} = \frac{\pi}{8}$, so $\theta = \frac{\pi}{4}$. $\tan\left(\frac{\pi}{8}\right) = \frac{1 - \cos\left(\frac{\pi}{4}\right)}{\sin\left(\frac{\pi}{4}\right)} = \frac{1 - \frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}} = \sqrt{2}-1$