Question

If cos (A+B) = cosAcos B – sinAsin B , find the value of cos 75

Answer 1

Answer:

Step-by-step explanation:

Cos 75 = Cos ( 30 + 45)  {Use Cos (A + B) identity}

            = Cos 30*cos 45 - Sin 30 Sin 45

            $= \frac{\sqrt{3}}{2}*\frac{1}{\sqrt{2}}-\frac{1}{2}*\frac{1}{\sqrt{2}}\\\\= \frac{\sqrt{3}}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}\\\\=\frac{\sqrt{3}-1}{2\sqrt{2}}\\\\=\frac{(\sqrt{3}-1)*\sqrt{2}}{2\sqrt{2}*\sqrt{2}}\\\\=\frac{\sqrt{3}*\sqrt{2}-\sqrt{2}}{2*2}\\\\=\frac{\sqrt{6}-\sqrt{2}}{4}$