Question 140

If tan(x + y)tan(x - y) = 1, then the value of $$tan(\frac{2x}{3})$$ is

tan(x+y)tan(x-y)=1
or tan(x+y)=cot(x-y)
or tan(x+y)=tan(90-x+y)
or x+y=90-x+y
or 2x=90
or x=45
Hence tan(2x/3) = tan 30 = $$1/\sqrt3$$

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