The most general value of θ which satisfies both the equations tan θ=√3 and operatornamecosec θ=-(2/√3) is-

Question

The most general value of θ which satisfies both the equations tan θ=√3 and operatornamecosec θ=-(2/√3) is- (A) n π+(4 π/3) ; n ∈ I (B) n π+(2 π/3) ; n ∈ I (C) 2 n π+(4 π/3) ; n ∈ I (D) 2 n π+(2 π/3) ; n ∈ I

Tardigrade Admin · Accepted Answer

tan θ=√3 and sin θ=-(√3/2) are both satisfied for only one value of θ=(4 π/3), θ ∈[0,2 π] ∴ aeneral solution is 2 n π+4 π

Q. The most general value of $θ$ which satisfies both the equations $tan θ = 3$ and $cosec θ = - \frac{2}{3}$ is-

$nπ + \frac{4 π}{3}; n \in I$

$nπ + \frac{2 π}{3}; n \in I$

$2 nπ + \frac{4 π}{3}; n \in I$

$2 nπ + \frac{2 π}{3}; n \in I$

$tan θ = 3$ and $sin θ = - \frac{3}{2}$ are both satisfied for only one value of $θ = \frac{4 π}{3}, θ \in [0, 2 π]$
$∴$ aeneral solution is $2 nπ + 4 π$

Q. The most general value of θ which satisfies both the equations tanθ=3​ and cosecθ=−3​2​ is-

nπ+34π​;n∈I

nπ+32π​;n∈I

2nπ+34π​;n∈I

2nπ+32π​;n∈I