It is given that $\cos \frac{9\pi}{8} = -\frac{m}{n}$. Express each of the following in terms

Question

It is given that $\cos \frac{9\pi}{8} = -\frac{m}{n}$. Express each of the following in terms of $m$ and $n$. $\cos \frac{9\pi}{8} + \cos \frac{5\pi}{4} + \cos \frac{11\pi}{8}$ $\sin \frac{9\pi}{8} + \sin \frac{5\pi}{4} + \sin \frac{11\pi}{8}$ $\cot\left(-\frac{\pi}{8}\right) + \cot\left(-\frac{\pi}{4}\right) + \cot\left(-\frac{3\pi}{8}\right)$ $\text{cosec}\hspace{0.5em} \frac{17\pi}{8} + \text{cosec}\hspace{0.5em} \frac{9\pi}{4} + \text{cosec}\hspace{0.5em} \frac{19\pi}{8}$

Accepted Answer

(i) $-\frac{\sqrt2}{2}-\frac{m+\sqrt{n^2-m^2}}n$ (ii) $-\frac{\sqrt2}{2}-\frac{m+\sqrt{n^2-m^2}}n$ (iii) $-\frac{n^2}{m\sqrt{n^2-m^2}}-1$ (iv) $\frac{n(m+\sqrt{n^2-m^2})}{m\sqrt{n^2-m^2}}+\sqrt2$

Trigonometry - Symmetry of Trigonometric Functions

Trigonometry - Symmetry of Trigonometric Functions

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