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Minimum value of (sec^4alpha)/(tan^2beta...

Minimum value of `(sec^4alpha)/(tan^2beta)+(sec^4beta)/(tan^2alpha),` where `alpha!=pi/2,beta!=pi/2,0

Text Solution

Verified by Experts

The correct Answer is:
8
Let `a =tan^2alpha,b-tan^2beta`
Given expression becomes
`((a+1)^2)/b+((b+1)^2)/a (age,bge0)`
`=(a^2+2a+1)/b+(b^2+2b+1)/a`
`=a^2/b+1/b+b^2/a+1/a+2(a/b+b/a)`
`ge4.4sqrt(a^2/b. 1/b b^2/(a.a))+2(2)`
`=4+4=8`
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