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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