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Evaluate tan π/8.

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√2 -1

answer is D.

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Detailed Solution

Let x = π/8

2x = π/4

We have tan 2x = 2 tan x /(1-tan2 x)

So tan π/4 = 2 tan π/8 /(1-tan2 π/8)

Put y = tan π/8

∴ 1 = 2y / (1-y2)

⇒ 1-y2 = 2y

⇒ y2+2y-1 = 0

y = (-2 ± √(4+4))/2

= (-2 ± 2√2)/2

= -1±√2

π/8 lies in the first quadrant. So tan π/8 is positive

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