If operatornamecosec A+ cot A=(11/2), then tan A is equal to

Question

If operatornamecosec A+ cot A=(11/2), then tan A is equal to (A) (21/22) (B) (15/16) (C) (44/117) (D) (117/43)

Tardigrade Admin · Accepted Answer

textcosec2 A- cot 2 A=1 ....(i) textcosec A+ cot A=(11/2)....(ii) dividing, we get textcosec A- cot A=(2/11) subtracting (ii) from (i), 2 cot A=(117/22) ⇒ tan A=(44/117)

Q. If $cosec A + cot A = \frac{11}{2}$ , then $tan A$ is equal to

$\frac{21}{22}$

$\frac{15}{16}$

$\frac{44}{117}$

$\frac{117}{43}$

$cosec^{2} A - cot^{2} A = 1$ ....(i)
$cosec A + cot A = \frac{11}{2}$ ....(ii)
dividing, we get $cosec A - cot A = \frac{2}{11}$
subtracting (ii) from (i), $2 cot A = \frac{117}{22}$
$\Rightarrow tan A = \frac{44}{117}$

Q. If cosecA+cotA=211​, then tanA is equal to

2221​

1615​

11744​

43117​