Given that $\operatorname{cosec} \alpha = x$ and $0^\circ

Question

Given that $\operatorname{cosec} \alpha = x$ and $0^\circ < \alpha < 90^\circ$, express each of the following in terms of $x$. $\sin \alpha$ $\tan (2\pi - \alpha)$ $\sec (\alpha - 90^\circ)$ $\cos (-\alpha)$ $\cot (90^\circ - \alpha)$ $\operatorname{cosec} (\pi - \alpha)$

Accepted Answer

(i) $\frac{1}{x}$ (ii) $\frac{\sqrt{x^2-1}}{x}$ (iii) $-\frac{\sqrt{x^2-1}}{x^2-1}$ (iv) $\frac{\sqrt{x^2-1}}{x^2-1}$ (v) $x$ (vi) $x$

Trigonometry - Symmetry of Trigonometric Functions

Trigonometry - Symmetry of Trigonometric Functions

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