If $c o s^{2} 45^{o} - c o s^{2} 30^{o} = x . c o s 45^{o} s i n 45^{o}$ then $x =$ ................

-1/2

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Solution

The correct option is A -1/2
$c o s^{2} 45^{o} - c o s^{2} 30^{o} = x c o s 45^{o} s i n 45^{o}$
$⟹ {(\frac{1}{\sqrt{2}})}^{2} - {(\frac{\sqrt{3}}{2})}^{2} = x \times \frac{1}{\sqrt{2}} \times \frac{1}{\sqrt{2}}$
$⟹ \frac{1}{2} - \frac{3}{4} = \frac{x}{2}$
$⟹ - \frac{1}{4} = \frac{x}{2}$
$⟹ x = - \frac{1}{2}$

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