`sec^(2) (tan^(-1) 2) + cosec^(2) (cot^(-1) 3)` is equal to

Options

A. 5
B. 13
C. 15
D. 6

Answer

C

Explanation

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`