Question

Value of Cos 75 degree is

Answer 1

The value of \( \cos 75^\circ \) can be calculated using the angle sum identity for cosine:

\[
\cos(75^\circ) = \cos(45^\circ + 30^\circ) = \cos(45^\circ) \cos(30^\circ) - \sin(45^\circ) \sin(30^\circ)
\]

Now, we know the values of the trigonometric functions at these angles:

- \( \cos(45^\circ) = \frac{\sqrt{2}}{2} \)
- \( \sin(45^\circ) = \frac{\sqrt{2}}{2} \)
- \( \cos(30^\circ) = \frac{\sqrt{3}}{2} \)
- \( \sin(30^\circ) = \frac{1}{2} \)

Plugging these values into the identity:

\[
\cos(75^\circ) = \left(\frac{\sqrt{2}}{2}\right)\left(\frac{\sqrt{3}}{2}\right) - \left(\frac{\sqrt{2}}{2}\right)\left(\frac{1}{2}\right)
\]

Calculating this gives:

\[
\cos(75^\circ) = \frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4} = \frac{\sqrt{6} - \sqrt{2}}{4}
\]

So, the value of \( \cos 75^\circ \) is:

\[
\cos(75^\circ) = \frac{\sqrt{6} - \sqrt{2}}{4}
\]