Math, asked by allysia, 11 months ago

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Answered by Pikaachu

+_+

-> Apply Cauchy Schwarz :

$\frac{ { (\sin {}^{2} (x)) }^{2} }{3} + \frac{ { (\cos {}^{2} (x)) }^{2} }{4} \geqslant \frac{( \sin {}^{2} (x) + \cos {}^{2} (x)) {}^{2} }{3 + 4}$

Fortunately, the equality holds here and so,

$\frac{\sin {}^{2} (x)}{3} = \frac{\cos {}^{2} (x)}{4}$

$= > \sin {}^{2} (x) = \frac{3}{7}$

Note that the given expression changes to :

$- > \frac{3}{2401} + \frac{4}{2401} = \frac{1}{343}$

Leave a comment :p

allysia: Thanks

allysia: but I'm only a 10th grade student

allysia: so i didn't get it

allysia: can you please explain it in a simpler way

Pikaachu: Umm, Cauchy Scwarz is an Inequality which says : For any Real a, b, c, d, ... , z and beyond ^^", we have :

Pikaachu: (a^2)/a' + (b^2)/b' + (c^2)/c' + ... + (z^2)/z' >= ( a + b + c + ... + z )^2/( a' + b' + c' + d' + e' + ... + z' )

Pikaachu: But the equality holds here and so, we have a special condition which helps us make our task easy ^^"

allysia: Hola human !!

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