Question

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

• A. $1$
• B. ${}_{-}^{+}\sqrt{5}$
• C. $\frac{1}{2}$
• D. ${}_{-}^{+}\sqrt{3}$

Answer 1

The correct option is B ${}_{-}^{+}\sqrt{5}$

$\cos A=2\sin A$

Dividing by $\sin A$on both the sides we get

$\cot A=2$ ...(i)

$cose{c}^{2}A=1+{\cot }^{2}A$

$cose{c}^{2}A=1+2^2$ ...(from i )

$cose{c}^{2}A=5$

Therefore

$cosecA=\pm \sqrt{5}$

Hence answer is B