How the property AM>or = GM used to get minimum value of the function......e,g for what condition of a and b does minimum value of a tan^2 x + b cot^2 x equals maximum value of a sin^2 x + b cos^2x
Ans) for min value of first func. we have..AM>or=GM
i.e a.tan^2x + b.cot^2x >or = 2(a.tan2x.bcot2x)^1/2 .....[ a+b/2 .or= (ab)^1/2 ] = 2(ab)^1/2hence min value of first function is 2(ab)^1/2
for second func.its in the form of a.siny + b.cosy whose max value =(a^2 + b^2)^1/2applying this we get the max. value of the func. as= (a^2 + b^2)^1/2
hence req. condition=> 2(ab)^1/2=(a^2 + b^2)^1/2 => 4ab = a^2 + b^2 => a^2 + b^2 - 4ab=0 (ANS)