The minimum value of `atan^2x+bcot^2x` equals the maximum value of `asin^2theta+bcos^2theta` where `a > b > 0.` The `a/b` is 2 (b) 4 (c) 6 (d) 8

Explanation

We know A.M. is always greater than or equal to G.M.

`:. (atan^2x+bcot^2x)/2 ge sqrt(atan^2xbcot^2x)`

`=> atan^2x+bcot^2x ge 2sqrt(ab) `

So, minimum value of `atan^2x+bcot^2x` is `2sqrt(ab).`


Now, `asin^2x+bcos^2x = asin^2x+b(1-sin^2x)`

`=(a-b)sin^2x+b`

So, maximum value of `asin^2x+bcos^2x = a-b+b = a`

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