If tan (a – b) = 1, sec (a + b) = 2/√3 and α,

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If tan (a – b) = 1, sec (a + b) = 2/√3 and α, β are positive, then the smallest value of a is :

tan (α – β) = 1 = tan 45°
⇒ α – β = 45° ..... (i)

sec (α + β) =	2	= sec 30°
	√3

⇒ α + β = 30° ..... (ii)
On adding (i) and (ii),
2α = 45° + 30° = 75°

⇒ a =	75	= 37	1°
	2		2

142	1°
	2

187	1°
	2