Find the principal value cosec-1 ((-2/√3))

Question

Find the principal value cosec-1 ((-2/√3))  (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 /2), (π /2)] - 0 ∴ Principal value of cosec-1 ((-2/√3)) is ((-π /3))

Q. Find the principal value $cose c^{- 1} (\frac{- 2}{3})$

$- \frac{π}{3}$

$\frac{π}{3}$

$\frac{π}{2}$

$- \frac{π}{2}$

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

Q. Find the principal value cosec−1(3​−2​)

−3π​

3π​

2π​

−2π​