Question

If cosec A + sin A = $5\frac{1}{5}$, the value of $cose{c}^{2}A+si{n}^{2}A$ is $25\frac{m}{25}$, m is

Answer 1

$cosecA+sinA=5\frac{1}{5}$
$cosecA+sinA=\frac{26}{5}$
Squaring both sides,
$cose{c}^{2}A+si{n}^{2}A+2cosecA\times sinA=\frac{26\times 26}{25}$
$cose{c}^{2}A+si{n}^{2}A+2=\frac{676}{25}$
$cose{c}^{2}A+si{n}^{2}A=\frac{676-60}{25}$
$cose{c}^{2}A+si{n}^{2}A=\frac{626}{25}$
$cose{c}^{2}A+si{n}^{2}A=25\frac{1}{25}$