1. Tardigrade
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  4. If a 2+ b 2=1, m 2+ n 2=1, then which of the following is true for all values of m , n , a , b -

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Q. If $a ^2+ b ^2=1, m ^2+ n ^2=1$, then which of the following is true for all values of $m , n , a , b$ -

Conic Sections

Solution:

Consider $ a =\cos \theta, b =\sin \theta$
$m =\cos \phi, n =\sin \phi$
Now, am $\pm bn =\cos \theta \cos \phi \pm \sin \theta \sin \phi$
$am \pm bn =\cos (\theta \mp \phi)$
$\therefore| am \pm bn | \leq 1$