( s i n A + c o s e c A ) 2 − ( s i n A − c o s e c A ) 2 = Options: A . &nbsp 0 B . &nbsp 1 C . &nbsp 2 D . &nbsp 4

Answer: Option D : D ⇒ ( sin A + cosec A ) 2 − ( sin A − cosec A ) 2 = 4 sin A cosec A as [ ( a + b ) 2 − ( a − b ) 2 = 4 a b ] now, ( sin A × cosec A = sin A × 1 sin A = 1 ) ∴ 4. sin A cosec A = 4 × 1 = 4

(sinA+cosecA)2−(sinA−cosecA)2=

Question

$(s i n A + c o s e c A)^{2} - (s i n A - c o s e c A)^{2} =$

Options:

A . 0

B . 1

C . 2

D . 4

Answer: Option D
:
D

$\Rightarrow (sin A + cosec A)^{2} - (sin A - cosec A)^{2}$

$= 4 sin A cosec A$
as $[(a + b)^{2} - (a - b)^{2} = 4 a b]$

now, $(sin A \times cosec A = sin A \times \frac{1}{sin A} = 1)$
$∴ 4. sin A cosec A = 4 \times 1 = 4$

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