Find the values of : cos 75° - Vidyadip

Question

Find the values of : cos 75°

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Answer

$\begin{aligned} & \cos 75^{\circ}=\cos \left(45^{\circ}+30^{\circ}\right) \\ & =\cos 45^{\circ} \cos 30^{\circ}-\sin 45^{\circ} \sin 30^{\circ} \\ & =\left(\frac{1}{\sqrt{2}}\right)\left(\frac{\sqrt{3}}{2}\right)-\left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{2}\right) \\ & =\frac{\sqrt{3}-1}{2 \sqrt{2}}\end{aligned}$

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