QuestionFind the value of $\tan \frac{\pi}{8} \cot \frac{3 \pi}{8} - \sec \frac{\pi}{8} \csc \frac{3 \pi}{8}$.

Studdy Solution
Finally, we can simplify the above expression to get the exact value of the given expression.
$$\frac{\sqrt{2}}{2}(\frac{\cos(\frac{\pi}{8}) - \sin(\frac{\pi}{8})}{\cos(\frac{\pi}{8})}) - \frac{2}{\sqrt{2}(\cos(\frac{\pi}{8}) + \sin(\frac{\pi}{8}))} = \sqrt{2} - \sqrt{2} =0$$So, the exact value of $\tan \frac{\pi}{8} \cot \frac{3 \pi}{8}-\sec \frac{\pi}{8} \csc \frac{3 \pi}{8}$ is0.