Which of the following is not the quadratic equation whose roots are cosec2θ and sec2θ is
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a
x2−6x+6=0
b
x2−7x+7=0
c
x2−4x+4=0
d
none of these
answer is D.
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Detailed Solution
sec2θ+cosec2θ=1cos2θ+1sin2θ=cos2θ+sin2θcos2θsin2θ=sec2θcosec2θnow,sec2θ+cosec2θ=2+tan2θ+cot2θ=4+(tanθ−cotθ)2≥4Hence, all equations can have roots sec2θ and cosec2θ