1.

If `(sec^4theta)/a+(tan^4theta)/b=1/(a+b),`then prove that `|b|lt=|a|`.

Answer» `(sec^4theta)/a+(tan^4b)/b=1/(a+b)=(sec^2theta-tan^2theta)/(a+b)`
`rArr(sec^4theta)/(a(a+b))[(a+b)sec^2theta-a]+tan^2theta/(b(a+b))[(a+b)tan^2theta+b]=0`
`rArra tan^2theta+bsec^2theta=0`
`rArrsin^2theta=-b/a`
Since`sin^2thetale1`
`rArrabs(b/a)le1orabsbleabsa`


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