Question

(sin ^A - cos^4 A +1 )/ sin^2A

simplify

Answer 1

$\frac{ \sin ^{4} (a) - \cos ^{4} (a) + 1 }{ \sin ^{2} (a) } \\ \\ \\ \\ => \frac{( \sin ^{2} (a) - \cos ^{2} (a))( \sin ^{2} (a) + \cos ^{2} (a) ) + 1 }{ \sin ^{2} (a) } \\ \\ \\ \\ => \frac{ - ( \cos ^{2} (a) - \sin ^{2} (a) ) + 1 }{ \sin ^{2} (a) }$

We know,
cos²A - sin²A = cos(2×A)

Applying formula,

$\frac{ - \cos (2a ) + 1 }{ \sin ^{2} (a) }$

We know,

$\frac{1 - \cos(a) }{2} = \sin ^{2} ( \frac{a}{2} )$

Applying formula,

$\frac{2 \sin ^{2} (a) }{ \sin ^{2} (a) }$

=> 2




Method 2 :


[ sin²A - cos²A + 1 ] / [ sin²A ]

=> 1 - cot²A + cosec²A



=> 1 + 1

=> 2