Q1 min value of f(x)=√a2cos2x+b2sin2x+√a2sin2x+b2cos2x
Q2 What is condition so that f(x)=ax3+bx2+cx+dsinx is one one fn
341That'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
1prophet 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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