The number of real values of (a,b) which satisfy the equation

$a - b = a \times b$ is?

0
infinite
1
2

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Put a = $\tan^{2} \theta$

b = $\sin^{2} \theta$

Simplifying

$\displaystyle \dfrac{sin^{2} x}{cos^{2} x} - sin^{2} x$

Taking LCM

$\displaystyle \dfrac{sin^{2}x(1 - cos^{2} x)}{cos^{2}x}$

$\displaystyle 1- cos^{2}x = sin^2 x$

$\displaystyle \dfrac{sin^{4}x}{cos^{2}x}$

Which equals

$\displaystyle tan^{2}x sin^{2}x$

which satifies the equation for all values of $\theta$ hence the answer is infinite