If tan245º – cos230º = x sin45º cos 45º then x = ?

Foundation

Mathematics Foundation

Introduction to Trigonometry

Question

If tan²45º – cos²30º = x sin45º cos 45º then x = ?

$\frac{- 1}{2}$

– 2

$\frac{1}{2}$

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$x = \frac{\tan^{2} 45 º - \cos^{2} 30 º}{\sin 45 º \cos 45 º} = \frac{1 - {(\frac{\sqrt{3}}{2})}^{2}}{(\frac{1}{\sqrt{2}} \times \frac{1}{\sqrt{2}})} = \frac{1 - \frac{3}{4}}{\frac{1}{2}} = \frac{1}{4} \times \frac{2}{1} = \frac{1}{2}$