Question

Please help i beg i never get these right

Answer 1

`\sin(105) = (\sqrt 2 + \sqrt 6)/(4)`

Explanation:

Given

`\sin(105^o)`

Required

Solve

Using sine rule, we have:

`\sin(A + B) = \sin(A)\cos(B) + \sin(B)\cos(A)`

This gives:

`\sin(105^o) = \sin(60 + 45)`

So, we have:

`\sin(60 + 45) = \sin(60)\cos(45) + \sin(45)\cos(60)`

In radical forms, we have:

`\sin(60 + 45) = (\sqrt 3)/(2) * (\sqrt 2)/(2) + (\sqrt 2)/(2) * (1)/(2)`

`\sin(60 + 45) = (\sqrt 6)/(4) + (\sqrt 2)/(4)`

Take LCM

`\sin(60 + 45) = (\sqrt 6 + \sqrt 2)/(4)`

Rewrite as:

`\sin(60 + 45) = (\sqrt 2 + \sqrt 6)/(4)`

Hence:

`\sin(105) = (\sqrt 2 + \sqrt 6)/(4)`