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The sum of distinct solutions of the equation $(4 \tan x + \tan^{2} x + 1) = 2 \sqrt{2} \sin (x + \frac{π}{4}) (1 + \tan^{2} x)$ in the interval $[0, π]$ is:

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detailed solution

Correct option is B

4tanx+sec2x=22sinx+π4sec2x⇒4sinxcosx+1=2sinx+cosx ⇒ 2sinx2cosx-1-2cosx-1=0 sinx=12,cosx =12⇒x=π6,5π6,π3

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The sum of distinct solutions of the equation 4tanx+tan2x+1=22sinx+π41+tan2x in the interval 0,π is:

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The sum of distinct solutions of the equation $(4 \tan x + \tan^{2} x + 1) = 2 \sqrt{2} \sin (x + \frac{π}{4}) (1 + \tan^{2} x)$ in the interval $[0, π]$ is: