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Q.

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

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a

π2

b

4π3

c

2π

d

7π6

answer is B.

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Detailed Solution

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: