Question

solve this sum please ​

Answer 1

$\sf \huge{\color{purple}{AnSwer:-}}$

$\sf\color{grey}{ \dag \: {cos}^{2} + {sin}^{2} x = 1}$

$: \implies \sf {sin}^{2} x = 1 - {cos}^{2} x$

$: \implies \sf {sin}^{2} x = 1 - \left( - \dfrac{1}{2} \right)^{2}$

$: \implies \sf {sin}^{2} x = 1 - \dfrac{1}{4}$

$: \implies \sf {sin}^{2} x = \dfrac{3}{4}$

$: \implies \sf {sin} x = \pm \dfrac{ \sqrt{3} }{2}$

x lies in third quadrant

$: \implies \sf {sin}x = - \dfrac{ \sqrt{3} }{2}$

$\sf \color{grey}{ \dag \: cosecx = \dfrac{1}{sinx}}$

$\color{red}{ : \implies \sf cosecx = - \dfrac{2}{ \sqrt{3} }}$