Let α and β be 2 real numbers which satisfy the equations cot 2 α- operatornamecosec2 β=(2 k /3)-5 text and - operatornamecosec2 α+ cot 2 β=( k 2/2), then sum of all possible value(s) of k is equal to

Question

Let α and β be 2 real numbers which satisfy the equations cot 2 α- operatornamecosec2 β=(2 k /3)-5 text and - operatornamecosec2 α+ cot 2 β=( k 2/2), then sum of all possible value(s) of k is equal to (A) -(4/3) (B) -6 (C) -1 (D) None

Tardigrade Admin · Accepted Answer

Adding the 2 equations, we get -2=(2 k/3)-5+(k2/2) (2 k/3)+(k2/2)-3=0 3 k2+4 k-18=0 Hence sum of all values of k=(-4/3)

Q. Let $α$ and $β$ be 2 real numbers which satisfy the equations $cot^{2} α - cosec^{2} β = \frac{2 k}{3} - 5 and - cosec^{2} α + cot^{2} β = \frac{k ^{2}}{2},$ then sum of all possible value(s) of $k$ is equal to

$- \frac{4}{3}$

-6

-1

None

Adding the 2 equations, we get
$- 2 = \frac{2 k}{3} - 5 + \frac{k ^{2}}{2}$
$\frac{2 k}{3} + \frac{k ^{2}}{2} - 3 = 0$
$3 k^{2} + 4 k - 18 = 0$
Hence sum of all values of $k = \frac{- 4}{3}$

Q. Let α and β be 2 real numbers which satisfy the equations cot2α−cosec2β=32k​−5 and −cosec2α+cot2β=2k2​, then sum of all possible value(s) of k is equal to

−34​

-6

-1

None

Adding the 2 equations, we get −2=32k​−5+2k2​ 32k​+2k2​−3=0 3k2+4k−18=0 Hence sum of all values of k=3−4​

Q. Let $α$ and $β$ be 2 real numbers which satisfy the equations $cot^{2} α - cosec^{2} β = \frac{2 k}{3} - 5 and - cosec^{2} α + cot^{2} β = \frac{k ^{2}}{2},$ then sum of all possible value(s) of $k$ is equal to

$- \frac{4}{3}$

Adding the 2 equations, we get
$- 2 = \frac{2 k}{3} - 5 + \frac{k ^{2}}{2}$
$\frac{2 k}{3} + \frac{k ^{2}}{2} - 3 = 0$
$3 k^{2} + 4 k - 18 = 0$
Hence sum of all values of $k = \frac{- 4}{3}$