The value of `sec^(2)(tan^(-1)2)+cosec^(2)(cot^(-1)3)` isA. 5B. 10C. 15D. 20

The value of `sec^(2)(tan^(-1)2)+cosec^(2)(cot^(-1)3)` isA. 5B. 10C. 1

1.	The value of `sec^(2)(tan^(-1)2)+cosec^(2)(cot^(-1)3)` isA. 5B. 10C. 15D. 20
Answer» We have `sec^(2)(tan^(-1)2)+cosec^(2)(cot^(-1)3)` `{sec(tan^(-1)2)}^(2)+{cosec(cot^(-1)3)` `=[sec(tan^(-1)2)^(2)+{cosec(cot^(-1)3)^(2)` `={sec(sec^(-1))sqrt(5)^(2)+cosec (cot^(-1))3/1}^(2)` `{sec(sec^(-1)2/1)}^(2)+(cosec(cosec^(-1))sqrt(10))^(2)` `=sqrt(5)^(2)+sqrt(10)^(2)=15`

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