Use formula
cos(A + B) = cos A cos B − sin A sin B
[tex]\cos{75^o}
\\ \cos{(45^o+30^o)}
\\ \cos{45^o}\cos{30^o}-\sin{45^o}\sin{30^o}
\\ \frac{ \sqrt{2} }{2} \times \frac{ \sqrt{3} }{2}-\frac{ \sqrt{2} }{2} \times \frac{1}{2}
\\ \frac{ \sqrt{6} }{4} -\frac{ \sqrt{2} }{4}
\\ \frac{ \sqrt{6}- \sqrt{2} }{4}
\\ \frac{ \sqrt{2}\sqrt{3}- \sqrt{2} }{4}
\\ \frac{ \sqrt{2}(\sqrt{3}- 1 )}{4} [/tex]
