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(a) The principal value of tan-1(-1) is

(b) If tan -1 (\(\frac{x-1}{x-2}\)) + tan-1 (\(\frac{x-1}{x+2}\)) = \(\frac{π}{4}\) then find the value of x

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(a) \(-\frac{π}{4}\)

⇒ \(\frac{2x^2 - 4}{-3}\) = 1 ⇒ 2x2 - 4 = -3 ⇒ x = ±\(\frac{1}{\sqrt2}\)

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