The value of tan2( sec-12)+ cot2(cosec-13) is

Question

The value of tan2( sec-12)+ cot2(cosec-13) is (A) 13 (B) 15 (C) 11 (D) none of these.

Tardigrade Admin · Accepted Answer

tan2 (sec-12 ) = sec2(sec-1 2) -1 cot2(cosec-1 3) = cosec2 (cosec-1 3)-1 ∴ given expression = (sec (sec-12))2 + (cosec(cosec-13))2 - 2 = (2)2 +(3)2-2 = 11

Q. The value of $tan^{2} (sec^{- 1} 2) + cot^{2} (cose c^{- 1} 3)$ is

13

15

11

none of these.

$t a n^{2} (se c^{- 1} 2) = se c^{2} (se c^{- 1} 2) - 1$
$co t^{2} (cose c^{- 1} 3) = cose c^{2} (cose c^{- 1} 3) - 1$
$∴$ given expression
$= (sec (se c^{- 1} 2))^{2} + (cosec (cose c^{- 1} 3))^{2} - 2$
$= (2)^{2} + (3)^{2} - 2 = 11$

Q. The value of tan2(sec−12)+cot2(cosec−13) is

13

15

11

none of these.

tan2(sec−12)=sec2(sec−12)−1 cot2(cosec−13)=cosec2(cosec−13)−1 ∴ given expression =(sec(sec−12))2+(cosec(cosec−13))2−2 =(2)2+(3)2−2=11

Q. The value of $tan^{2} (sec^{- 1} 2) + cot^{2} (cose c^{- 1} 3)$ is

$t a n^{2} (se c^{- 1} 2) = se c^{2} (se c^{- 1} 2) - 1$
$co t^{2} (cose c^{- 1} 3) = cose c^{2} (cose c^{- 1} 3) - 1$
$∴$ given expression
$= (sec (se c^{- 1} 2))^{2} + (cosec (cose c^{- 1} 3))^{2} - 2$
$= (2)^{2} + (3)^{2} - 2 = 11$