`underset(xrarrpi/6)("lim") (2sin^(2)x+ sinx - 1)/(2sin^(2)x-3 sinx + 1)` किसके बराबर है ?

Options

A. `-1/2`
B. `-1/3`
C. `-2`
D. `-3`

Explanation

दिया है,
`underset(xrarr(pi)/(6))("lim") (2sin^(2)x + sinx - 1)/(2sin^(2) x - 3 sin x + 1)`
` = underset(xrarr(pi)/(6))("lim") (2sin^(2)x + 2 sinx - sinx- 1)/(2sin^(2) x - 2 sinx - sin + 1)`
` = underset(xrarr(pi)/(6))"lim" (2 sin (sinx + 1) - (sinx + 1))/(2 Sinx (sinx - 1) - 1(sinx - 1))`
` = underset(xrarr(pi)/(6))("lim") ((sinx + 1)(2sinx - 1))/((sinx - 1)(2sinx -1))`
` = underset(xrarr(pi)/(6))("lim") (sinx + 1)/(sinx - 1) = ((1)/(2) + 1)/((1)/(2) - 1) = (3/2)/(-1/2) = - 3`