fns sbts

1) sqaure both sides

u get min as a+b

That's the triangle law in vector spaces:

|v_1| + |v_2| \ge |v_1+v_2|

So here v_1 = (a \cos x, b \sin x); v_2 = (b \cos x, a \sin x)

Hence

RHS = |v_1+v_2| =\sqrt {(a+b)^2(\cos^2 x + \sin^2x)} = |a+b|

This inequality is in fact application of the Minkowski Inequality

prophet sir ,
can u give a small theory an applications of minkowski inequality
because in many places , especially in definite integral , i have seen the posts where u have made use of that
or can u provide any link
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