Question

Use a half-angled identity to find the exact value of sin 75 degrees

Answer 1

[A]
`\frac{\sqrt{2 + √(3) } }{2}`

Answer 2

`\sin 75\degree=\frac{\sqrt{2+√(3)}}{2}`

Explanation:

The haf-angle formula is given by:

`\sin (1)/(2)\theta =\sqrt{(1-\cos \theta)/(2) }`

`\sin 75\degree=\sin (1)/(2)(150\degree)`.

This implies that:

`\sin (1)/(2)(150\degree) =\sqrt{(1-\cos 150\degree)/(2) }`

`\sin (1)/(2)(150\degree) =\sqrt{(1--(√(3))/(2))/(2)}`

`\sin (1)/(2)(150\degree) =\sqrt{(2+√(3))/(4)}`

We simplify the square root to obtain:

`\sin (1)/(2)(150\degree)=\frac{\sqrt{2+√(3)}}{2}`