Question

If $\sin A=\frac{\sqrt{3}}{2}$, find the value of $2{\cot }^{2}A-1$.

Answer 1

$\sin A=\frac{\sqrt{3}}{2}\left(\text{Given}\right)$

$2{\cot }^{2}A-1$

$=2{\cot }^{2}A+2-2-1$

$=2({\cot }^{2}A+1)-3$

$=2cose{c}^{2}A-3$

$=\frac{2}{{\sin }^{2}A}-3$

$=2{\left(\frac{2}{\sqrt{3}}\right)}^2-3$

$=\frac{8}{3}-3$

$=\frac{-1}{3}$