Answer:
1) tan 157.5=[tex]\frac{1-cos315}{sin315}[/tex]
2) sin 165 = [tex]\sqrt{\frac{1-cos330}{2} }[/tex]
3) sin² 157.5 = [tex]1/2(1-cos315)[/tex]
4) cos 330 = [tex]1-2sin^{2}(165)[/tex]
Step-by-step explanation:
1) [tex]\sqrt{\frac{1-cos330}{2} }= sin330/2 = sin 165[/tex]
By the identity [tex]sin(A/2)=\sqrt{\frac{1-cosA}{2} } }[/tex]
2) [tex]1-2sin^{2}(165)=cos2(165) = cos330[/tex]
By the identity 1-2sin²A = cos2A
3) [tex]\frac{1-cos315}{sin315}=tan(315/2)=tan(157.5)[/tex]
By the identity [tex]\frac{1-cosA}{sinA}=tan(A/2)[/tex]
4) 1/2(1-cos315) = 1/2[1-(1-2sin²315/2)] = sin²157.5
By the identity cos2A = 1-2sin²A
