Find the value of
$4 {t a n}^{2} 45 + 35 s i n 60 - c o s 30$

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Solution

$4 {tan}^{2} 45^{\circ} + 35 sin 60^{\circ} - cos 30^{\circ}$

We know that $tan 45^{\circ} = 1$ , $sin 60^{\circ} = \frac{\sqrt{3}}{2}$ and $cos 30^{\circ} = \frac{\sqrt{3}}{2}$

$= 4 \times 1^{2} + 35 \times \frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2}$

$= 4 + \frac{35 \sqrt{3} - \sqrt{3}}{2}$

$= 4 + \frac{34 \sqrt{3}}{2}$

$= 4 + 17 \sqrt{3}$

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