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If sec x =- (13)/(12) and (pi)/(2) lt x ...

If `sec x =- (13)/(12)` and `(pi)/(2) lt x lt pi ,` find the value of `sin 2x`

A

`(60)/(169)`

B

`(-60)/(169)`

C

`(120)/(169)`

D

`(-120)/(169)`

Text Solution

Verified by Experts

The correct Answer is:
D
Since x lies in Quadrant II , we have sin `x gt 0` cos x ` lt 0` and tan `x lt 0`
Now sec `x =(-13)/(12) rArr " cos " x = (1)/(" sec x ") =(-12)/(13)`
`:. " sin " x = + sqrt(1- "cos"^(2) ) x =+ sqrt(1- (144)/(169)) = + sqrt((25)/(169)) =(5)/(13)`
And tan `x= (sin x)/(cos x) =(5)/(13) xx ((-13)/(13)) =((-13)/(12)) = (-5)/(12)`
`(i) " sin " 2x = 2 " sin x cos x "`
`={2xx (5)/(13) xx ((-12))/(13)}= (-120)/(169)`
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