Question
; then the general solution of A=
Hint:
A general solution is one which involves the integer ‘n’ and gives all solutions of a trigonometric equation.
The correct answer is:
We have, tan(π/4 + A/2) + tan (π/4 - A/2) = 4/√3
=> (1+ tanA/2)/(1-tanA/2) + (1-tanA/2)/(1+tanA/2) = 4/√3
=> {(1 + tan²A/2 + 2tanA/2) + (1 + tan²A/2 - 2tanA/2)}/ (1- tan²A/2) = 4/√3
=> {2(1+ tan²A/2)}/(1 - tan²A/2) = 4/√3
=> (1-tan²A/2)/(1+tan²A/2) = √3/2
=> cos 2(A/2) = cos π/6
=> cosA = cos π/6
=> A = 2nπ ± π/6.
Hence, the correct option is C.
tan (π/4 + A) = (1+tanA)/(1-tanA).
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