` "cosec"x =-2` का व्यापक हल है -

Options

A. ` x = npi (-1)^(n)* (5 pi)/3 ,n in Z`
B. ` x = npi (-1)^(n)* (7pi)/6,n in Z`
C. ` x = 2npi (-1)^(n)* (pi)/6,n in Z`
D. ` x = npi + (pi)/2 ,n in Z`

Answer

B

Explanation

` "cosec" x = -2 = - "cosec" pi//6`
`rArr "cosec" x = "cosec" (pi+ pi/6) ` अथवा ` "cosec" (2pi = pi/6)`
` rArr "cosec" x = "cosec" ((7pi)/6)` अथवा ` "cosec" ((11pi)/6)`
` rArr x = (7pi)/6 " अथवा " x = (11pi)/6`
अतः समीकरण `"cosec"x = -2` का मुख्य हल ` x = (7pi)/6`
अथवा ` (11pi)/6`
तथा व्यापक हल ` x = npi (-1)^(n)* (7pi)/6,n in Z`