Question

Find each exact value. Use a sum or difference identity. sin 75°

Answer 1

`\sin(75^(\circ)) \\ \\ =\sin(30^(\circ)+45^(\circ)) \\ \\ =\sin 30^(\circ) \cos 45^(\circ)+\cos 30^(\circ) \sin 45^(\circ) \\ \\ =(1)/(2) \cdot (\sqrt 2)/(2)+(\sqrt 3)/(2) \cdot (\sqrt 2)/(2) \\ \\ =\boxed{(\sqrt 6+\sqrt 2)/(4)}`