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Number of solutions of the equation $4 \sin^{2} x + \tan^{2} x + \cot^{2} x + \cos e c^{2} x = 6$ in $[0, π]$ is

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Correct option is B

We have 4sin2x+tan2x+cot2x+cosec2x=64sin2xcos2x1cos2x+tan2x+cot2x+1+cot2x=64tan2xsec2x+tan2x+2cot2x=5Let tanx=t⇒4t21+t2+t2+2t2=54t4+t4(1+t2)+2(1+t2)t2(1+t2)=54t4+t4+t6+2+2t2=5t2+5t4⇒t6−3t2+2=0 clearly +1,-1 are roots using sythetic division⇒t2−1t4+t2−2=0⇒t2=1,t2=−2(not possible) ⇒t2=1⇒t=±1 ⇒tanx=±1 ⇒x=π4,3π4

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