Question

If $\cos A=2\sin A$ find the value of $cosecA$

• A. 1
• B. $\pm \sqrt{5}$
• C. $\frac{1}{2}$
• D. $\pm \sqrt{3}$

Answer 1

Answer: (B)

$\pm \sqrt{5}$

$\because \cos A=2\sin A$
$\therefore {\cos }^{2}A=4{\sin }^{2}A$
$⟹1-{\sin }^{2}A=4{\sin }^{2}A$
$5{\sin }^{2}A=1$
$\therefore \sin A=\pm \frac{1}{\sqrt{5}}$
$⟹cosecA=\pm \sqrt{5}$