Question

Sec²(tan⁻¹2)+cosec²(cot⁻¹3)=............,Select Proper option from the given options.
(a) 15
(b) 6
(c) 13
(d) 25

Answer 1

we have to find the value of sec²{tan^-1(2)}+cosec² {cot^-1(3)}

sec²{tan^-1(2)}+cosec² {cot^-1(3)} = [sec{tan^-1(2)}]² + [cosec{cot^-1(3)}]²

Let tan^-1 (2) = A
tanA = 2 => secA = √5 .......(1)

similarly, cot^-1(3) = B
cotB = 3 => cosecB = √10...........(2)

[sec{tan^-1(2)}]² + [cosec{cot^-1(3)}]² = [secA]² + [cosecB]²

from equations (1) and (2),

= √5² + √10²

= 5 + 10 = 15

hence, option (a) is correct.

Answer 2

HELLO DEAR,



GIVEN:-
Sec²(tan-¹2)+cosec²(cot-¹3) = ?

let tan-¹2 = x so, tanx = 2 => secx = √5

let cot-¹3 = y so, coty = 3 => cosecy = √10


so, Sec²(tan-¹2)+cosec²(cot-¹3)= sec ²x + cosec ²y

=> (secx)² + (cosecy)²

=> (√5)² + (√10)²

=> 5 + 10

=> 15

hence, option (a) is correct,


I HOPE ITS HELP YOU DEAR,
THANKS