Principal value of operatornamecosec-1((-2/√3)) is equal to

Question

Principal value of operatornamecosec-1((-2/√3)) is equal to (A) -(π/3) (B) (π/3) (C) (π/2) (D) -(π/2)

Tardigrade Admin · Accepted Answer

Let cosec -1((-2/√3))=θ ⇒ cosec θ=(-2/√3)=-cosec (π/3)=cosec ((-π/3)) ⇒ θ=(-π/3) ∈[(-π/3), (π/2)]- 0 ∴ Principal value of cosec -1((-2/√3)) is ((-π/3))

Q. Principal value of $cosec^{- 1} (\frac{- 2}{3})$ is equal to

$- \frac{π}{3}$

$\frac{π}{3}$

$\frac{π}{2}$

$- \frac{π}{2}$

Let $cosec^{- 1} (\frac{- 2}{3}) = θ$
$\Rightarrow cosec θ = \frac{- 2}{3} = - cosec \frac{π}{3} = cosec (\frac{- π}{3})$
$\Rightarrow θ = \frac{- π}{3} \in [\frac{- π}{3}, \frac{π}{2}] - {0}$
$∴$ Principal value of $cosec^{- 1} (\frac{- 2}{3})$ is $(\frac{- π}{3})$

Q. Principal value of cosec−1(3​−2​) is equal to

−3π​

3π​

2π​

−2π​