If cot[] = 1 and sec[] = [ - 5 3]

Question

If cot$$\alpha$$ = 1 and sec$$\beta$$ = $$ - {5 \over 3}$$

Accepted Answer

$\because \cot \alpha=1, \quad \alpha \in\left(\pi, \frac{3 \pi}{2}\right)$

then $\tan \alpha=1$

and $\sec \beta=-\frac{5}{3}, \quad \beta \in\left(\frac{\pi}{2}, \pi\right)$

then $\tan \beta=-\frac{4}{3}$

$\therefore \tan (\alpha+\beta)=\frac{\tan \alpha+\tan \beta}{1-\tan \alpha \cdot \tan \beta}$

$$
\begin{aligned}
&=\frac{1-\frac{4}{3}}{1+\frac{4}{3}} \\
&=-\frac{1}{7}
\end{aligned}
$$

$$
\alpha+\beta \in\left(\frac{3 \pi}{2}, 2 \pi\right) \text { i.e. fourth quadrant }
$$

Solutions · 1