Question

Simplify the following without using a calculator:

(a) \(2 \sin 22,5^{\circ} \cdot \cos 22,5^{\circ}\)
(b) \(2 \sin 75^{\circ} \cdot \cos 75^{\circ}\)
(c) \(2 \sin \left(-15^{\circ}\right) \cdot \cos \left(-15^{\circ}\right)\)
(d) \(4 \sin 105^{\circ} \cdot \cos 105^{\circ}\)
(e) \(\sin 165^{\circ} \cdot \cos 165^{\circ}\)
(f) \(\cos ^2 15^{\circ}-\sin ^2 15^{\circ}\)
(g) \(\cos ^2 15^{\circ}+\sin ^2 15^{\circ}\)
(h) \(\left(\cos 15^{\circ}-\sin 15^{\circ}\right)^2\)
(i) \(1-2 \sin ^2 15^{\circ}\)
(j) \(2 \cos ^2 75^{\circ}-1\)
(k) \(2 \sin ^2 22,5^{\circ}-1\)
(1) \(1-2 \cos ^2 105^{\circ}\)