Question

prove that :-
$\sqrt{ \sin ^{4} ( {x} ) + 4\cos^{2} {x} } = 2 - \sin ^{2} (x)$
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Answer 1

$\sqrt{ { \sin }^{4} x + 4 { \cos}^{2} x} \\ \\ \\ = \sqrt{ { \sin}^{4}x + 4 - 4 { \sin}^{2}x } \\ \\ \\ = \sqrt{ { ({ \sin }^{2} x)}^{2} - 2(2)( { \sin }^{2} x) + {2}^{2} } \\ \\ \\ = \sqrt{ {( 2 - { \sin }^{2} x) }^{2} } \\ \\ \\ = 2 - { \sin }^{2} x \\ \\ \\ = rhs$

a^2 - 2ab + b^2 = ( a - b )^2

sin^2x + cos^2x = 1

THANKS