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`

Explanation

LHS


`tan ^{2}(sec ^{-1} 2)+cot ^{2}({cosec}^{-1} 3) `
`
=sec ^{2}(sec ^{-1} 2)-1+{cosec}^{2}({cosec}^{-1} 3)-
1[sec ^{2} theta-tan ^{2} theta=1 ; {cosec}^{2} theta-cot ^{2} theta=1] `
`
=[sec (sec ^{-1} 2)]^{2}-1+[{cosec}({cosec}^{-1} 3)]^{2}-1=2^{2}-1+4^{2}-1=4-1+9-1= `
`
3+8=11= { RHS }`

ii)

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