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Cauchy - Schwarz Inequality

From the Cauchy - Schwarz Inequality,

$f(\theta) \leq \sqrt{A^{2} + B^{2}} \cdot \sqrt{sin^{2}\theta + cos^{2}\theta}$

$f(\theta) \leq \sqrt{100} \cdot 1$

$f(\theta) \leq \boxed{10}$

at\quad \theta =\tan ^{ -1 }{ \sfrac { A }{ B } } \ given\quad func.\quad has\quad max\quad value.putting\quad \quad \theta =\tan ^{ -1 }{ \sfrac { A }{ B } } in\quad given\quad eqn.we\quad get-\ A\sin { (\tan ^{ -1 }{ \sfrac { A }{ B } } ) } +B\cos { (\tan ^{ -1 }{ \sfrac { A }{ B } } ) } =f(\theta )\ as\quad we\quad see\quad f(\theta )\quad is\quad max\quad either\quad at\quad \theta =90\quad or\quad 0\ for\quad 90\quad given\quad condition\quad will\quad not\quad satisfy\quad so\quad we\quad take\quad \theta =0\ so\quad \tan ^{ -1 }{ \sfrac { A }{ B } } =0\ thus\quad A=0\quad thus\quad from\quad given\quad condition\quad B=10\ thus\quad max\quad value\quad of\quad f(\theta )=B\cos { 0 } =B=10 copy above and paste in Daum equation editor..