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

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Solution

$sin A + c o s e c A = 2$
Squaring both sides, we get
$\Rightarrow {(sin A + c o s e c A)}^{2} = 4$
$\Rightarrow {sin}^{2} A + c o s e c^{2} A + 2 = 4$
$\Rightarrow {sin}^{2} A + c o s e c^{2} A = 2$
Hence, the answer is $2.$

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