If sin A + cosec A = 2; find the value of $s i n^{2} A + c o s e c^{2} A$ .

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Solution

$s i n A + c o s e c A = 2$
Squaring both sides,
$(s i n A + c o s e c A)^{2} = 2^{2}$
$s i n^{2} A + c o s e c^{2} A + 2 s i n A . c o s e c A = 4$
$s i n^{2} A + c o s e c^{2} A + 2 = 4$
$s i n^{2} A + c o s e c^{2} A = 2$

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