Answer:
tan(2x) = 2√2
Step-by-step explanation:
You want tan(2x) when tan(x) is -2/√2 and x is a 4th-quadrant angle.
Double angle
The tangent double-angle identity is ...
tan(2x) = 2tan(x)/(1 -tan(x)²)
For tan(x) = -2/√2, this gives ...
tan(2x) = 2(-2/√2)/(1 -(-2/√2)²) = -2√2/(1 -2)
tan(2x) = 2√2
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