If sinα= p , then the quadratic equation whose roots are tanα2 , cotα2 is

sin α=Ptan α2+cot α2=2cosec α=2Ptanα2 cot α2=1tanα2,cotα2 are roots of eqnsx2-2Px+1=0 ⇒ Px2=2Px+P=0

If sinα= p , then the quadratic equation whose roots are tanα2 , cotα2 is

sin α=Ptan α2+cot α2=2cosec α=2Ptanα2 cot α2=1tanα2,cotα2 are roots of eqnsx2-2Px+1=0 ⇒ Px2=2Px+P=0

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$I f \sin α = p, t h e n t h e q u a d r a t i c e q u a t i o n w h o s e r o o t s a r e \tan \frac{α}{2}, c o t \frac{α}{2} i s$

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$p x^{2} - 2 x + p = 0$

$p x^{2} - x + p = 0$

$p x^{2} + 2 x + p = 0$

$p x^{2} + x + p = 0$

answer is A.

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Detailed Solution

$\begin{array}{rcl} \sin α & = & P \\ \tan \frac{α}{2} + \cot \frac{α}{2} & = & 2 cosec α = \frac{2}{P} \\ \tan \frac{α}{2} \cot \frac{α}{2} & = & 1 \end{array}$

$\tan \frac{α}{2}, \cot \frac{α}{2}$ are roots of eqns

$\begin{array}{rcl} x^{2} - \frac{2}{P} x + 1 & = & 0 \\ \Rightarrow & {Px}^{2} = 2 Px + P = 0 \end{array}$

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If sinα= p , then the quadratic equation whose roots are tanα2 , cotα2 is

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$I f \sin α = p, t h e n t h e q u a d r a t i c e q u a t i o n w h o s e r o o t s a r e \tan \frac{α}{2}, c o t \frac{α}{2} i s$