Prove that: `sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15` and `tan^2(sec^(-1)2)+cot^2(cos e c^(-1)3)=11`

Answer

`15`

Explanation

`sec ^{2}(tan ^{-1} 2)+cosec ^{2}(cot ^{-1} 3) `

`=1+tan ^{2}(tan ^{-1} 2)+1+cot ^{2}(cot ^{-1} 3) `


`=1+[tan (tan ^{-1} 2)]^{2}+1+[cot (cot ^{-1} 3)]^{2}`
`=1+2^{2}+1+3^{2}=15`