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sec^(2)(tan^(-1)4)+cosec^(2)(cot^(-1)3) ...

`sec^(2)(tan^(-1)4)+cosec^(2)(cot^(-1)3) =`

A

5

B

13

C

15

D

6

Text Solution

Verified by Experts

Let `tan^(-1) 2 = alpha " or " tan alpha = 2`
and `cot^(-1) 3 = beta " or " cot beta = 3`
`sec^(2) (tan^(-1) 2) + cosec^(2) (cot^(-1) 3)`
`= sec^(2) alpha + cosec^(2) beta`
`= 1 + tan^(2) alpha + 1 + cot^(2) beta`
`= 2 + (2)^(2) + (3)^(2) = 15`
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