If tan2 45° – cos230° = x sin 45° cos 45° then x = ?


If tan2 45° – cos230° = x sin 45° cos 45° then x = ?

(a) 2

(b) –2

(c) $\frac{1}{2}$

(d) $-\frac{1}{2}$



As we know that,

$\cos 45^{\circ}=\frac{1}{\sqrt{2}}$

$\cos 30^{\circ}=\frac{\sqrt{3}}{2}$

$\tan 45^{\circ}=1$

$\sin 45^{\circ}=\frac{1}{\sqrt{2}}$

By substituting these values, we get

$\tan ^{2} 45^{\circ}-\cos ^{2} 30^{\circ}=x \sin 45^{\circ} \cos 45^{\circ}$


$\Rightarrow 1-\frac{3}{4}=\frac{x}{2}$

$\Rightarrow \frac{4-3}{4}=\frac{x}{2}$

$\Rightarrow \frac{x}{2}=\frac{1}{4}$

$\Rightarrow x=\frac{1}{2}$

Hence, the correct option is (c).


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