Question

Select the correct answer

Answer 1

1) tan 157.5=
`(1-cos315)/(sin315)`

2) sin 165 =
`\sqrt{(1-cos330)/(2) }`

3) sin² 157.5 =
`1/2(1-cos315)`

4) cos 330 =
`1-2sin^(2)(165)`

Explanation:

1)
`\sqrt{(1-cos330)/(2) }= sin330/2 = sin 165`

By the identity
`sin(A/2)=\sqrt{(1-cosA)/(2) } }`

2)
`1-2sin^(2)(165)=cos2(165) = cos330`

By the identity 1-2sin²A = cos2A

3)
`(1-cos315)/(sin315)=tan(315/2)=tan(157.5)`

By the identity
`(1-cosA)/(sinA)=tan(A/2)`

4) 1/2(1-cos315) = 1/2[1-(1-2sin²315/2)] = sin²157.5

By the identity cos2A = 1-2sin²A