Question

PROBLEMITA RETADOR -TRIGONOMETRIA ​

Answer 1

Es fácil ver que

$\theta = \dfrac{135}{2}\\ \\ \\\tan\dfrac{135}{4}=\csc \dfrac{135}{2}-\cot \dfrac{135}{2}\\ \\ \\\tan\dfrac{135}{4}=\sqrt{\dfrac{2}{1-\cos 135}}-\sqrt{\dfrac{1+\cos 135}{1-\cos 135}}\\ \\\\\tan\dfrac{135}{4}=\dfrac{2}{\sqrt{2+\sqrt2}}-\sqrt{\dfrac{2-\sqrt{2}}{2+\sqrt2}}\\ \\ \\\boxed{\tan\dfrac{135}{4}= \sqrt{2}-1 + \sqrt{2(2-\sqrt{2})}}$