The maximum value of the expression ∣(√(sin^2 x+2a^2 )) −(√(2a^2 −1−cos^2 x)) ∣ where a and x real numbers is−−−


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Question Number 171593 by cortano1 last updated on 18/Jun/22

$T h e m a x i m u m v a l u e o f t h e$ $e x p r e s s i o n ∣ \sqrt{\sin^{2} x + 2 a^{2}} - \sqrt{2 a^{2} - 1 - \cos^{2} x} ∣$ $w h e r e a a n d x r e a l n u m b e r s i s - - -$
Commented by infinityaction last updated on 18/Jun/22

$f o r m a x i m u m v a l u e$ $2 a^{2} - 1 - \cos^{2} x = 0$ $\cos^{2} = 2 a^{2} - 1$ $1 - \sin^{2} x = 2 a^{2} - 1$ $\sin^{2} x + 2 a^{2} = 2$ $s o$ $∣ \sqrt{2} - 0 ∣ = \sqrt{2} (m a x i m u m v a l u e)$
Commented by cortano1 last updated on 18/Jun/22

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