Find the Value of Cos 75 Degrees ?

Solution :

The value of cos 75 degrees is \(\sqrt{3} – 1\over 2\sqrt{2}\).

Proof :

We will write cos 75 as cos (45 + 30).

By using formula cos (A + B) = cos A cos B – sin A sin B,

cos (45 + 30) = cos 45 cos 30 – sin 45 sin 30

\(\implies\) cos 75 = \(1\over \sqrt{2}\) \(\times\) \(\sqrt{3}\over 2\) – \(1\over \sqrt{2}\) \(\times\) \(1\over 2\)

\(\implies\) cos 75 = \(\sqrt{3} – 1\over 2\sqrt{2}\)

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