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Question

If tan (A − B) = 1 and sec (A + B) = 23, the smallest positive value of B is

(a) 25 π24
(b) 19 π24
(c) 13π24
(d) 11 π24

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Solution

(b) 19 π24
Given:tan(A-B)=1 and sec(A+B) =23A-B=π4...(1) and A+B=π6...(2)Adding these equations we get: 2A=π4+π6A=5π24Smallest possible value of B=π-5π24=19π24.

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