Find the value of sin2a, if tana=-12/5 in the fourth quadrant

Recall the following identities:




from which we get




Since is in the fourth quadrant we know that should be positive, so when we take the square root here, we should take the positive root.



Now recall that



and since is in the fourth quadrant, we expect to be negative. So,



One final identity:



from which we get

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