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If pi/2 lt alpha lt pi, pi lt beta lt 3p...

If `pi/2 lt alpha lt pi, pi lt beta lt 3pi/2; sin alpha = 15/17 `and `tan beta = 12/5`, then the value of `sin(beta - alpha)` is

A

`-(171)/(221)`

B

`-(21)/(221)`

C

`(21)/(221)`

D

`(171)/(221)`

Text Solution

Verified by Experts

The correct Answer is:
D
Given ,`sinalpha=(15)/(17),tanbeta=(12)/(5)`
`rArrcosalpha=(8)/(17),sinbeta=(12)/(13)andcosbeta=-(5)/(13)`
`rArrpiltbetalt(3pi)/(2)`
`thereforecosbeta=-(5)/(13)`
`sin(beta-alpha)=sinbetacosalpha-cosbetasinalpha=(171)/(221)`.
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