Question

Explain how to find the exact value of cos(75°).

Answer 1

Answer:

$\cos(75 \degree) = \cos(45 \degree + 30\degree) \\ \\ = \cos(45\degree) \cos(30\degree) - \sin(45\degree) \sin(30\degree) \\ \\ = ( \frac{1}{ \sqrt{2} } ).( \frac{ \sqrt{3} }{2} ) - ( \frac{1}{ \sqrt{2} } ).( \frac{1}{2} ) \\ \\ = \frac{ \sqrt{3} }{2 \sqrt{2} } - \frac{1}{2 \sqrt{2} } \\ \\ = \frac{ \sqrt{3} - 1}{2 \sqrt{2} } \\ \\ = \frac{0.73205}{2.828427} \\ \\ = 0.2588$